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Cold guided beams of polar molecules [Elektronische Ressource] / Michael Motsch

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Cold Guided Beams ofPolar MoleculesMichael MotschTemperature (K)1 5 10 201.0HO2DO0.8 2HDO0.60.40.20.00 50 100 150 200Velocity (m/s)DissertationMax-Planck-Institut fur Quantenoptik, Garchingand Physik Department, Technische Universitat Munchen December 2009Physik Departmentechnische Universit?t M?nchenTMPQSignal of guided moleculesCover illustration: The gure on the cover shows velocity distributions of coldguided water molecules produced by electrostatic velocity ltering. These distri-butions illustrate the di erent sensitivity of the water isotopologs H O, D O, and2 2HDO to external electric elds.Technische Universitat Munchen Max-Planck-Institut fur QuantenoptikCold Guided Beams ofPolar MoleculesMichael MotschVollstandiger Abdruck der von der Fakultat fur Physik der Technischen Universitat Munchen zur Erlangung des akademischen Grades einesDoktors der Naturwissenschaften (Dr. rer. nat.)genehmigten Dissertation.Vorsitzender : Univ.-Prof. Dr. W. ZwergerPrufer der Dissertation : 1. Hon.-Prof. Dr. G. Rempe2. Univ.-Prof. Dr. St. PaulDie Dissertation wurde am 30.10.2009 bei der Technischen UniversitatMunchen eingereicht und durch die Fakultat fur Physik am 11.12.2009angenommen.AbstractThis thesis reports on experiments characterizing cold guided beams of polar mo-lecules which are produced by electrostatic velocity ltering.

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Published 01 January 2009
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Cold

Guided

Beams

oleculesMrolaP

Michael

Motsch

Dissertation

Quantenoptik,ur¨fMax-Planck-Institut

Physik

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Department,TechnischeUniversit¨at

December

2009

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TechnischeUniversit¨atM¨unchen
Quantenoptikur¨fMax-Planck-Institut

ColdPolarGuidedMoleculesBeamsof

MotschMichael

Vollst¨andigerAbdruckdervonderFakult¨atf¨urPhysikderTechnischen
Universit¨atM¨unchenzurErlangungdesakademischenGradeseines

DoktorsderNaturwissenschaften(Dr.rer.nat.)

Dissertation.genehmigten

:rsitzenderoV

Univ.-Prof.Dr.W.Zwerger

Pr¨uferderDissertation:1.Hon.-Prof.Dr.G.Rempe
2.Univ.-Prof.Dr.St.Paul

DieDissertationwurdeam30.10.2009beiderTechnischenUniversit¨at
M¨uncheneingereichtunddurchdieFakult¨atf¨urPhysikam11.12.2009
angenommen.

Abstract

Thisthesisreportsonexperimentscharacterizingcoldguidedbeamsofpolarmo-
leculeswhichareproducedbyelectrostaticvelocityfiltering.Thisfilteringmethod
exploitstheinteractionbetweenthepolarmoleculesandtheelectricfieldprovided
byanelectrostaticquadrupoleguidetoextractefficientlytheslowmoleculesfroma
thermalreservoir.FormoleculeswithlargeandlinearStarkshiftssuchasdeuter-
atedammonia(ND3)orformaldehyde(H2CO),fluxesofguidedmoleculesof1010–
1011molecules/sareproduced.Thevelocitiesofthemoleculesinthesebeamsare
intherangeof10–200m/sandcorrespondtotypicaltranslationaltemperaturesof
afewKelvin.ThemaximumvelocityoftheguidedmoleculesdependsontheStark
shift,themolecularmass,thegeometryoftheguide,andtheappliedelectrodevolt-
age.Althoughthesourceisoperatedinthenear-effusiveregime,thenumberdensity
oftheslowestmoleculesissensitivetocollisions.Atheoreticalmodel,takinginto
accountthisvelocity-dependentcollisionallossofmoleculesinthevicinityofthe
nozzle,reproducesthedensityoftheguidedmoleculesoverawidepressurerange.
Acarefuladjustmentofpressureallowsanincreaseinthetotalnumberofmolecules,
whilstyetminimizinglossesduetocollisionsofthesought-forslowmolecules.This
isanimportantissueforfutureapplications.
Electrostaticvelocityfilteringissuitedfordifferentmolecularspecies.Thisis
demonstratedbyproducingcoldguidedbeamsofthewaterisotopologsH2O,D2O,
andHDO.Althoughthesearechemicallysimilar,theyshowlinearandquadratic
Starkshifts,respectively,whenexposedtoexternalelectricfields.Asaresult,the
fluxofHDOislargerbyoneorderofmagnitude,andthefluxoftheindividual
isotopologsshowsacharacteristicdependenceontheguidingelectricfield.
Theinternal-statedistributionofguidedmoleculesisstudiedwithanewlydevel-
opeddiagnosticmethod:depletionspectroscopyofformaldehyde.First,ultraviolet
absorptionspectroscopyoftheA˜1A2←X˜1A1transitionofformaldehydeisper-
formedinaroom-temperaturegastoextractmolecularconstants.Thesefindings
areusedtoaddresssinglerotationalstatesofguidedmolecules.Sincetheformalde-
hydemoleculesdissociateuponultravioletexcitation,thelaser-frequency-dependent
decreaseinthenumberofguidedmoleculesallowstoextractthepopulationofin-
dividualrotationalstatesinthebeam.Withthesourcetemperaturesetto155K,
populationsofrotationalstatesexceeding10%areobserved,whichvalidatesthe
theoreticalmodelofvelocityfiltering.
Finally,Rayleighscatteringintoanopticalcavityisinvestigatedasanalternative,
non-destructivedetectionmethodforcoldmolecules.Comparingtherateofscatter-
ingintothefundamentalcavitymodetothatintothesamemodeunderfree-space
conditions,anenhancementbyafactorofupto38isobservedforroom-temperature
gases.ThisPurcell-likeenhancementisexplainedbyinterferenceofelectromagnetic
fieldsscatteredbyaclassicaldrivendipoleoscillatorintheresonator.

v

Zusammenfassung

DievorliegendeArbeitberichtet¨uberExperimentemitkaltengef¨uhrtenMo-
lek¨ulstrahlen,diemittelsderelektrostatischenGeschwindigkeitsfilterungerzeugt
werden.DabeiwirddieWechselwirkungzwischenpolarenMolek¨ulenundeinem
elektrischenQuadrupolf¨uhrungsfeldausgenutzt,umdielangsamenMolek¨uleaufeffi-
zienteWeiseauseinemthermischenReservoirzuextrahieren.F¨urMolek¨ulewieAm-
moniak(ND3)oderFormaldehyd(H2CO),dieeinegroßelineareStark-Verschiebung
erfahren,lassensichFl¨ussevon1010–1011Molek¨ulen/srealisieren.Diegef¨uhrtenMo-
lek¨ulehabenGeschwindigkeitenvon10–200m/s,waseinerTemperaturvoneinigen
Kelvinentspricht.DieH¨ochstgeschwindigkeitderMolek¨ulewirddurchihreStark-
VerschiebungundMasse,dieGeometriederMolek¨ulf¨uhrungsowiedieangelegte
Elektrodenspannungbestimmt.ObwohldieMolek¨ulzufuhraufdennaheffusivenBe-
reicheingestelltwird,reagiertdieZahlderlangsamstenMolek¨uleempfindlichauf
St¨oße.EinModell,dassolchegeschwindigkeitsabh¨angigenVerlustedurchSt¨oßeim
BereichderD¨useber¨ucksichtigt,beschreibtdieDichtedergef¨uhrtenMolek¨ule¨uber
einenweitenDruckbereich.EineOptimierungdesDruckeserlaubt,dieGesamtzahl
derMolek¨ulezuerh¨ohen,w¨ahrendVerlustederlangsamstenMolek¨uledurchSt¨oße
minimiertwerden.Diesistf¨urzuk¨unftigeAnwendungenwichtig.
DieVielseitigkeitderelektrostatischenGeschwindigkeitsfilterungwirddurchdie
Erzeugungkaltergef¨uhrterStrahlenderWasserisotopologeH2O,D2OundHDO
demonstriert.Obwohlchemischsehr¨ahnlich,zeigensieimexternenelektrischen
Feldeinenlinearenbzw.quadratischenStark-Effekt.DerFlussankaltemHDOist
daherumeineGr¨oßenordnungh¨oher,undderFlussderIsotopologezeigtjeweils
einecharakteristischeAbh¨angigkeitvomangelegtenelektrischenF¨uhrungsfeld.
DieVerteilungderinternenZust¨andedergef¨uhrtenMolek¨ulewirdmittelsei-
nerneuentwickeltenMethode,derEntv¨olkerungsspektroskopievonFormaldehyd,
untersucht.Zun¨achstwirdzurBestimmungvonMolek¨ulkonstantenineinemther-
mischenFormaldehydgasAbsorptionsspektroskopiedesultravioletten¨Ubergangs
A˜1A2←X˜1A1durchgef¨uhrt.DamitlassensichdanneinzelneRotationszust¨ande
imgef¨uhrtenMolek¨ulstrahlansprechen.DaFormaldehydmolek¨ulebeiultravioletter
Anregungdissoziieren,l¨asstderEinbruchimSignaldergef¨uhrtenMolek¨uleaufdie
BesetzungeinzelnerZust¨andeimStrahlschließen.BeieinerTemperaturderQuelle
von155KwerdenZustandsbev¨olkerungenvon¨uber10%beobachtet,wasdieim
VorfeldentwickelteTheoriederGeschwindigkeitsfilterungeindeutigbest¨atigt.
MitderRayleigh-StreuungineinenoptischenResonatorwirdeinealternative,
nichtdestruktiveDetektionsmethodef¨urkalteMolek¨uleuntersucht.DieRateder
StreuungindiefundamentaleResonatormodeistf¨urthermischeGaseumeinen
Faktor38h¨oheralsjeneindieselbeModeimfreienRaum.DiesedemPurcell-
Effektentsprechende¨Uberh¨ohungwirddurchInterferenzdervoneinemklassischen
getriebenenDipolgestreutenelektromagnetischenWellenbeschrieben.
vi

tstenCon

Abstract

Zusammenfassung

v

vi

1Coldpolarmolecules1
1.1Applicationsofcoldpolarmolecules...................2
1.1.1Coldchemistryandcoldcollisions................2
1.1.2Quantuminformationscience..................4
1.1.3Precisionspectroscopy......................5
1.2Productionofcoldpolarmolecules...................6
1.2.1Indirectmethods:Forgingmolecularbondsbetweenultracold
atoms...............................7
1.2.2Directmethods:Controllingtranslationalandinternalmolec-
ularmotion............................8
1.3ApproachoftheRempegrouptoproducecoldmolecules.......11
1.3.1History,developments,andextensionsoftheelectricguide..11
1.4Thisthesis.................................13

2Electrostaticvelocityfilteringandguidingofpolarmolecules15
2.1Theoryofelectrostaticvelocityfilteringofpolarmolecules......16
2.1.1Velocitydistributionsinthethermalsource..........18
2.1.2Cutoffvelocitiesintheelectricguide..............18
2.1.3Fluxofguidedmolecules.....................19
2.2Experimentalsetup............................19
2.3Velocity-filteringexperiments......................21
2.4Theflux-densitymystery.........................22
2.5Velocitydistributionofguidedmolecules................26

3Collisionaleffectsintheformationofcoldguidedbeamsofpolar
29molecules3.1Measurementsofcollisionaleffects....................29
3.2Pressuredependenceofvelocityfiltering................30
3.3Modelofvelocityfilteringincludingcollisionallosses..........33
3.4Electrode-voltagedependenceofvelocityfiltering...........35

4

5

6

7

3.5Velocitydistributionsofguidedmolecules................38
3.6Summary.................................40

Coldguidedbeamsofwaterisotopologs41
4.1Starkshiftofthewaterisotopologs...................42
4.1.1CalculationofStarkshifts....................43
4.1.2DiscussionofStarkshifts.....................48
4.2Calculationofthefluxofguidedmolecules...............55
4.3Experimentalprocedure.........................57
4.4Electrode-voltagedependence......................60
4.5Velocitydistributions...........................62
4.6Summary.................................64

Internal-statethermometrybydepletionspectroscopy67
5.1Experimentalsetup............................68
5.2Room-temperatureabsorptionspectroscopyofformaldehyde.....70
5.2.1Formaldehyde-spectroscopysetup................70
5.2.2Resultsanddiscussion......................73
5.3Internal-statedistributionofguidedformaldehydemolecules.....77
5.3.1Depletionspectroscopyofindividualrotationalstates.....77
5.3.2Internal-statedistributionintheguidedbeam.........80
5.4Summary.................................82

Cavity-enhancedRayleighscattering83
6.1Experimentalsetup............................85
6.2Cavitymodespectrum..........................87
6.3Classicalwave-interferencemodelofcavityenhancement.......89
6.3.1Theintracavityfield.......................89
6.3.2Comparisontofree-spacescattering:ThePurcellfactor....91
6.4Cavity-finessedependenceofRayleighscattering............95
6.4.1Influenceofthecavityfinesseonthespectralprofiles.....95
6.4.2Cavity-finessedependenceofthescatteredpower.......96
6.5Summary.................................97

99okOutlo7.1Extensionsandapplicationsofelectrostaticvelocityfilteringandguid-
ing.....................................100
7.1.1Spectroscopyofcoldmolecules..................100
7.1.2Collisionexperimentswithcoldmolecules...........101
7.2OngoingdevelopmentsintheRempegroup...............102
7.2.1Electrostaticextractionofmoleculesfromacryogenicbuffer-
gassource.............................103
7.2.2Opto-electricalcoolingofpolarmolecules............105

viii

AGuiding-efficiencyreconstructionforthedifferentwaterisotopologs107
A.1Concentrationsofwaterisotopologsinjectedintothequadrupoleguide107
A.2Detectionofcoldguidedwaterisotopologs...............111

yBibliograph

PublicationsofList

Danksagung

ix

115

137

139

x

1Chapter

olarpColdmolecules

Thefieldofcoldandultracoldatomshasreceivedalotofattentioninthelasttwo
decades.Theuseoflightforcesforcoolingofatoms,constitutingamainingredient
forthisresearchfield,wasproposedalreadyearlyon[Ash70,H¨an75,Win75,Ash78].
Shortlyaftertheadventofstable,narrow-linewidthlasers,lasercoolingoftrapped
ions[Neu78,1Win78]and,onlyfewyearslater,offreeatomsinthegasphasewas
demonstrated.Thedevelopmentoftheselaser-coolingtechniqueshaspavedtheway
forinvestigationsinthefieldoffundamentallight-matterinteractionsandultracold
quantumgases.Therefore,the1997NobelPrizeinPhysicswasjointlyawarded
otodsS.toChcoou,lC.andtrapCohen-Tatomsannoudji,withlaserandW.light”.D.ThePhillips“fordemonstrationdevofelopmentofBose-Einsteinmeth-
condensation(BEC)indiluteatomicgaseswasaresearchhighlightemployingthese
newly-developedcoolingtechniques.Tohonourthis,the2001NobelPrizeinPhysics
wasawardedtoE.A.Cornell,W.Ketterle,andC.E.Wieman“fortheachievement
ofBose-Einsteincondensationindilutegasesofalkaliatoms,andforearlyfunda-
mentalstudiesofthepropertiesofthecondensates”2.Onlyfewyearslater,thecold
atomcommunityroutinelyusessuchdenseandcoldatomicgasestrappedinoptical
latticestostudyproblemsarisinginsolid-statesystemssuchas,e.g.,thesuperfluid
[toBil08,Mott-insulatorRoa08].Ultracoldphaseatomictransitiongases[Gre02can,alsoVol06be,Vusedol07to]orstudyAndersonphenomenalocalizationrelated
tosuperconductivitysuchastheBEC-BCScrossover[Blo08,Gio08].Here,ultracold
atomicfermionsarepairedupbyasuitablytailoredmagneticinteractiontoforma
bosoniccompoundsystemresemblingaCooperpair.
Thedegreesoffreedomintheseatomicsystemsare,however,limitedtoelectronic
excitationsandtodifferentnuclearspinstates.Anaturaldevelopmentwouldbeto
extendthisfieldofresearchbyincludingmolecules,whichofferadditionaldegrees

1Forareviewofthesedevelopmentssee,e.g.,the1997Nobel-PrizelecturebyW.D.Phillips
[Phi98]andreferencestherein.
2ForareviewofthedevelopmentsontheroutetoBECincoldatomicgasessee,e.g.,the
2002Nobel-PrizelecturesbyE.A.CornellandC.E.Wieman[Cor02],W.Ketterle[Ket02],and
n.itherereferences

1

2

Coldmoleculesolarp

offreedomsuchasvibrationalandrotationalexcitations.Furthermore,especially
polarmoleculesaresubjecttothelong-range,anisotropicdipole-dipoleinteraction,
whichisofspecialinterestforcoldchemistryandalsopromisestopavetheroad
fornewdevelopmentsinquantuminformationscienceandquantumsimulations.
Inthefollowingsection,someresearchfieldswhichareexpectedtobenefitfrom
theavailabilityofsamplesofcoldpolarmoleculesarepresented:coldchemistry,
quantuminformationscience,andmeasurementsoftheelectron’selectricdipole
moment.Forabroaderoverview,thereaderisreferredtosomerecentspecialissues
oncoldandultracoldpolarmoleculesinEur.Phys.J.D[Doy04],J.Phys.B[Dul06],
andNewJ.Phys.[Car09].

1.1Applicationsofcoldpolarmolecules
Beforediscussingpossibleapplicationsofcoldpolarmolecules,adefinitionofthe
termmagnitude“cold”oftheshallinbegivteractionen[bDoetwy04een,theKre08].moleculesThecandoldranegimeexternallyisreached,appliedwhenelectricthe
orfieldsmagneticandfieldmoleculabrecomesdipolemomencomparabletstothisthehappthermalensattemenergyp.Feraturesortypicaloflabaroundoratory1K.
Attheseenergies,thedistributionofinternalmolecularstatesisstronglypurifiedas
comparedmoleculestoareanstronglyensembleatinfluencedroombytemptheerature.contributionTherefore,ofsinglecollisionsrotationalbetweenstacoltes,d
whichcanexhibitsignificantlydifferingcollisionproperties.However,differentpar-
tialoncewathevesultrconacoldtributeregimetoisthereacscathedteringattproypicalcesstempintheeraturescoldofregime.around1ThismK.cInhangesthis
i.e.,regimeonlyaacollisionsinglebetpartialweenwatheveconmoleculestributescantobethefullyscatteringdescribedprobycess.s-wFavoreevenscattering,lower
temperaturesthequantum-degenerateregimeisapproached.Here,effectscausedby
inquanteractiontumbetstatisticsweensuchparticles.asthePauliexclusionprinciplestronglycontributetothe

1.1.1Coldchemistryandcoldcollisions
Thedynamicsofchemicalreactionsisoftengovernedbyabarrierinthereaction
coordinate.Toovercomethisreactionbarrieranddrivethereaction,energymust
befedtothereactants.Inthecoldregimewithcollisionenergiescorresponding
toatemperatureontheorderof1K,thereisnotenoughenergyavailabletoover-
comesuchabarrier.Nevertheless,exothermicchemicalreactionswithabarrierare
predictedtotakeplaceevenundersuchconditionsduetoquantum-mechanicaltun-
neling,aswastheoreticallyshownforthereactionF+H2→FH+H[Bal01,Bal02].
Theinfluenceofrotationalexcitationonthedynamicsofchemicalreactionswas
investigatedbyJ.J.Gilijamseetal.,whomeasuredthecrosssectionofthecolli-
sionbetweencoldOHradicalsandXeatoms[Gil06].Intheirexperiment,coldOH

1.1Applicationsofcoldpolarmolecules

3

moleculeswereproducedbyStarkdecelerationandcollidedwithasupersonicXe
jet.ByadjustingthefinalvelocityoftheOH−1moleculesintherangeof33–700m/s,
thecollisionenergywasvariedfrom50–400cm.Atcollisionenergiesexceeding
theenergycorrespondingtothelowestrotationalexcitationsoftheOHmolecule,
newreactionchannelsopenedintheinelasticcollision,asobservedfromtheappear-
anceofpopulationinexcitedrotationalstatesofOH.B.C.Sawyeretal.reported
onasimilarstudyofcollisionsbetweencoldmoleculesandanatomicormolecular
gasjet[Saw08].InthisexperimentasupersonicbeamofHeorD2wascollided
withmagneticallytrappedOHmolecules.Inthistrap,OHmoleculesatadensity
of106cm−3andatemperatureof70mKwerestoredfor430ms.Thecollisionen-
ergywasadjustedbyheatingthevalveforthesupersonicexpansionofHeorD2,
whichtunedthebeam’svelocity.Thisway,center-of-massenergiesof60–230cm−1
(145–210cm−1)wereaccessibleforthecollisionHe–OH(D2–OH).Whenthecollision
energywasreducedbelowthethresholdenergyforrotationalexcitationofOH,asud-
dendropinthelossrateofmoleculesfromthetrapwasfound,indicatingareduced
collisioncrosssectionwhenthisinelasticchannelisnotavailable.Evenmoreexam-
plesforcoldchemistrycanbefoundbyincludingalsoionicspecies.Thereaction
Ca++CH3F→CaH++CH2FwasstudiedbyS.Willitschetal.usingalaser-cooled
crystalofCa+ionsstoredinalinearPaultrapandaslowbeamofCH3Fproduced
byelectrostaticvelocityfilteringandguiding[Wil08a,Wil08b,Bel09a].J.Mikosch
etal.studiedthenucleophilicsubstitutionreactionCl−+CH3I→I−+CH3Cl,by
crossedmolecularbeamimagingtoclarifythereactionpathway[Mik08a,Mik08b].
Incoldcollisions,theinteractionenergybetweenthemoleculeandanexternally
appliedelectricormagneticfieldcanbeonthesameorderofmagnitudeasthe
collisionenergy.CalculationsofscatteringratesforOHradicalsshowthatthe
long-rangedipole-dipoleinteractiondominatescollisionsbetweenpolarmolecules
[Avd02].Therefore,formationratesintheselow-energychemicalreactionsareex-
pectedtobemodifiableandfinallyevencontrollablebyapplyingsuitableelectric
andmagneticfields[Kre05,Kre08,Bel09b].Asaprototypesystem,thehydrogen
abstractionchannelinthereactionH2CO+OH→HCO+H2Owastheoretically
studied[Hud06].Thissystemisofspecialinterestsincebothinvolvedspecies,
formaldehyde(H2CO)moleculesandOHradicals,canbeproducedattunableen-
ergiesbyStarkdecelerationandevenelectrostaticallytrapped.Inthisreaction,the
barrierisadjustablebyanexternalelectricfield,suchthatsuppressioneffectsinthe
reactionratecouldbeobservable.
Externallyappliedfieldscanalsoplayanimportantroleforthelifetimeofmolecu-
lesinelectricormagnetictraps.Forexample,calculationsshowthatsuitableelectric
offsetfieldscanpreventtraplossesbyinelasticcollisions[Boh01].Anotherexample
arecollisionsbetweencold17O2andatomic3Heinthepresenceofmagneticfields
[Vol02].Suchconditionsarepresentinsetupscombiningbuffer-gascoolingwith
magnetictrapping.Forbuffer-gascooledandmagneticallytrappedNHmolecules,
inelasticcollisionswithHewereidentifiedastrap-lossmechanisms[Cam07,Cam09].

4

scienceinformationtumQuan1.1.2

olarpColdmolecules

Oneofthekeychallengesinquantuminformationscienceistofindsystemsper-
mittingfastgateoperations,strongandcontrollablecouplingsbetweenindividual
qubits,and,atthesametime,longdecoherencetimes.Molecules,ingeneral,pos-
sessarichinternallevelstructure,includinglong-livedrotationalstateswhichseem
adequatetoencodequantuminformationin.D.DeMilleproposedtouseanarray
ofpolarmoleculesstoredinsuitableelectricfieldsasanarchitectureforaquan-
tumcomputer[DeM02].Here,theinformationisencodedintheorientationofthe
moleculardipolemomentwithrespecttoanexternallyappliedelectricfield.At
thesametimetheelectricdipolemomentpromotesacouplingbetweenindividual
qubits.Togetherwithsingle-qubitrotations,thesecontrolledcouplingsconstitutea
necessityforuniversalquantum-gateoperations.C.M.TeschandR.deVivie-Riedle
suggestedtousevibrationallyexcitedmoleculesforquantuminformationprocess-
ing[Tes02].Here,thedifferentvibrationalmodesofamoleculeareusedasqubits,
whilethequantum-logicoperationsaredrivenbyshapedfemtosecondlaserpulses.
A.Andre´etal.proposedtocouplepolarmoleculestoamicrowavestriplinecavity
[And06,Cˆot06].Whilethemolecularrotationalstatesareusedforstorageofquan-
tuminformation,thestrongdipolecouplingtothecavity-enhancedelectricfield
permitsanefficientmeansfortransferringtheinformationtotheresonator.This
way,thecouplingbetweendistantqubitscanbemediatedoverlargedistancesby
themicrowavecavityfield.Furthermore,thestrongcouplingofthemoleculestothe
intracavityfieldcanbeusedforsidebandcoolinginthetrap[Vul01,Wal08,Lei09].
P.Rabletal.suggestedtouseasetupcombiningmolecularensemblesandaCooper-
pairboxcoupledtoastriplinecavity[Rab06].WhiletheCooper-pairboxcanbe
usedforfastgateoperations,themolecules,offeringlongdecoherencetimes,serve
asaquantummemory.Thecouplingbetweenthesetwoisachievedviathestripline
cavity,whichcanalsobeusedtoconverttheinformationstoredinthemolecular
ensembletoaflyingqubitinthemicrowavefield.Molecularensemblescoupledto
suchstriplinecavitiescanalsobeusedtoimplementamany-qubitsystem,where
theinformationcaneitherbestoredinthecollectiveexcitationoftheensemble
[Tor08a]orinaspatialphasevariationovertheensemble[Tor08b].
Anotherproposedapplicationofcoldpolarmoleculesistheiruseforquantum
simulations.Theideaofusingawell-controllablequantumsystemtosimulatethe
unknownbehaviorofanotherquantumsystemdatesbacktoR.Feynman[Fey82,
Bul09].Ultracoldatomicormoleculargaseswhicharetrappedinopticallattices
couldbeusedtosimulatethebehaviorofsolid-statesystemsdescribedbydifferent
Bose-Hubbardmodels[Lew07].Especiallypolarmoleculesareidealtoolstosim-
ulatetheHamiltoniansofsuchsystems.AsproposedbyA.Michelietal.,lattice
spinsystemscanberealizedbyconsideringdiatomicpolarmoleculestoredinan
opticallatticewherethespinismappedonasinglevalenceelectron[Lew06,Mic06].
Theanisotropicspin-spininteractionsarethenreplacedbythedipole-dipoleinter-
actionbetweenthepolarmoleculesincombinationwithmicrowaveexcitationsand

1.1Applicationsofcoldpolarmolecules

5

spin-rotationcouplings.Bychoosingsuitablearrangementsandorientationsofthe
moleculardipoleswithrespecttoeachother,theHamiltonianscorrespondingto
differentphysicalsystemscanthenbesimulated.
Asshownintheprecedingparagraph,awholevarietyofproposalsforapplica-
tionsofcoldpolarmoleculesinquantuminformationscienceexists.However,the
challengeremainstopreparesuitablesamplesofcoldpolarmolecules.Formany
oftheabove-mentionedschemes,themoleculesmustbelocalizedtoahighdegree,
e.g.,inanopticaldipoletraporanopticallattice,andpreparedinawell-defined
initialstate.Furthermore,gateoperationsdemandforthewell-controlledcoupling
ofinternalstatesbyphase-coherentlightfields.

1.1.3Precisionspectroscopy:TestsofCPTsymmetry
Duepretationtotheirofrictheirhspinternalectra,moleculesstructure,arewhichexcellenatfirsttseemscandidatestoforcomplicateprecisionthetesintster-of
CPTsymmetry(C:chargeconjugation,P:paritytransformation,T:timereversal).
talThefirstsymmetriesexperimenwastaltheobservdemonstrationationofofanaviolationasymmetryofinanytheofβthe-decathreeyoffpundamen-olarized
60theCowbeakyC.inS.Wteraction,uetasal.[Wsuggestedu57].bThisyT.D.asymmetryLeeandisC.causedN.Ybangy[paritLee56y].Fviolationurther-in
more,thisobservationalreadyhintedatacombinedviolationofCandPsymmetry
[ofLee57the,Wneutralu57]Kwhichmesonwassystemconfi[rmedChr64by].theHowevobserver,ifationCPofCPsymmetryviolationisbrokinen,thealsodecaTy
constituensymmetrytmofustquannotbtumefieldconservedtheoryto[Pfulfillau55the].CPTtheorem,consideredanessential
Thesearchforapermanentelectricdipolemoment(EDM)oftheneutronorofthe
electronsymmetryb[oundPur50in,atomsHun91,orinBol08].moleculeP.sG.rH.epresenSandetsrsonepoinptedossibleouttestthatofTtheandeffectCPTof
theeffectsEDM(theofanenhancemenelectrontinanscalesasatomic∝α2Zsystem3,withisαbsignificaneingtlythefineenhancedstructurebyrelativisticconstant
andTherefore,Zthentheuclearsofarcmostharge)asprecisecomparedtestsoftothethefreelectron’seelectron’sEDMhavEDMeb[eenSan65p,erformCom07edin].
199205bheaoundvyforatomsthesuchaselectron’sTl[EDMReg02of]dore<3Hg×[Gri10−0929].ecmThese(eisexptheerimenelementsgivtaryeanchaupprge,er
e=−381.602×10−19C).Whilethestandardmodelofparticlephysicspredictsavalueof
10intheecmrangefor<the10−26electr−10on’s−28eEDM,cm[Ctheoriesom99].beyTheondthesensitivitystandardinthesemodelexppredicterimenvtsalueshas
Evthereforeenlargerreachedaenhancemenleveltwhicheffectsseemsarepreseneligiblettoinpolardiscriminatemoleculesbetwwhiceenhsucmakhesmothemdels.
veryMey08,attractivMey09e,forTar09the].searcThehforenergytheshiftEDMdueoftothetheelectronelectron’s[Hin97,EDMdDeM00e,,whichKoz02an,
deatom∙P(orEa)∙Emoleculeint,whereexpEineriencestisintheanatomicexternallyorappliedmolecular-structure-depelectricfieldEaenden,istginiventernalby

6

pColdmoleculesolar

theelectricinternalfield,andelectricP(Eafield)isoftheheavydegreeatomsofpandolarizationmoleculesofthecanatomhavoresimilarmolecule.size,Whilethe
degreeofpolarizationismuchlargerinmolecules.Inatoms,differentelectronic
energyelectroniclevelsstatesmustarebealreadmixedymixedtobyinducetheacphemicalolarization.bond.TInpherefore,olaronlymolecules,rotationtheseal
statesmustbemixedtoinduceapolarization.Duetotheirproximityontheenergy
thescale,samthiseresultsmagnitude.inaFlargerurthermore,degreepofolarpolarizationmoleculesforhavanetheappliedadvantelectricageofbfieldeingof
lesssensitivetostraymagneticfields.Firstexperimentswithmolecules(YbF)have
btheeenexpperimenerformedtsandemploareyingalreadyatoms[closeHud02to].reacInthishingaexperimensensitivitt,yamolecularcompatiblebeamwith
effusingoutofahotovencontainingYbandAlF3hasbeenused.Theuseofacold,
slowbeamofYbFisexpectedtobringanadditionalsensitivityduetothelonger
interactiontimeswiththeprobinglaserfields[Sau06a,Sau06b].

1.2Productionofcoldpolarmolecules

Thecomplexinternalstructureofmolecules,whichfacilitatesthepromisingappli-
cationsdiscussedintheprecedingparagraphs,necessitatesnewcoolingschemes.
Lasercooling,whichhasenabledtheproductionofultracoldatomicsamples,relies
oniterativelyscatteringphotonsonamoreorlessclosedcyclingtransition[Met99].
Ingeneral,theplethoraofinternalstatesaccessibleinmoleculesuponspontaneous
decayfromanelectronicallyexcitedstaterendersstandardlaser-coolingandre-
pumpingschemesunfeasible.Nevertheless,theremightbeafewspecialmolecular
systemswithveryfavorableFranck-Condonfactors.Intheserarecases,thenumber
ofvibrationalstateswithintheelectronicgroundstatewhicharepopulatedupon
spontaneousdecaymightberestrictedtoasufficientlysmallnumbertomakelaser
coolingpossible[DR04,Stu08].
Inrecentyearsavarietyoftechniqueshasbeendevelopedwhichallowforthe
productionofmolecularsamplesinthecoldandeventheultracolddomain(see,
e.g.,thespecialissuesoncoldmoleculesinEur.Phys.J.D[Doy04],J.Phys.B
[Dul06],andNewJ.Phys.[Car09]).Thesemaybesubdividedintwogroups:On
theonehandside,thereareindirectmethodswhichstartwithultracoldatomicsam-
plesandproduceboundatompairs,i.e.,molecules,usingeithermagneticFeshbach
resonances[K¨oh06]orphotoassociation[Jon06].Sincethesemoleculesareproduced
incollisionsofultracoldatompairsby“controlledchemistry”,nokineticenergyre-
leaseoccurs.Themoleculesproducedbythesemethodsarethereforetranslationally
atroughlythesametemperatureastheatoms.Sinceacouplingmustbemediated
betweenaboundmolecularstateandapairoffreeatoms,themoleculesproduced
thatwaytypicallyoccupyhighlyexcitedinternalmolecularstates.Ontheother
handside,directmethodsstartwith“real”molecules,eitherfromsupersonicbeam
sourcesorthermalreservoirs.Differenttechniquesaimatthecontroloftheexter-

1.2Productionofcoldpolarmolecules

7

naldegreesofmotionbysuitablytailoredelectric[Bet99,Ran03,vdM08],magnetic
[Nar08b],oroptical[Ful04]fields.Coolingoftheinternalmotionisachievedei-
therinasupersonicexpansion[Pau00]orbycollisionswithacryogenicbuffergas
[Wheliumei98].nanoColddropletsmolecules[Toe98can,Sti01also].beSinceprotheseducedbymoleculesimplanintrintationsiofcallyinmoleculesteractinwithto
theheliumenvironment,thislattercoolingmechanismfallsoutsidethescopeofthis
thesisandisnotfurtherdiscussedhere.

1.2.1Indirectmethods:Forgingmolecularbondsbetween
atomsultracoldMagneticFeshbachresonancesoccurincollisionsbetweentwoatoms,when
anincidentopenchanneliscoupledtoaclosedmolecularchannel.Incollisions
betweenultracoldatomsthestatesinvolvedaredifferenthyperfinestatescoupled
bysomesortofinteraction.Duetotheirdifferentmagneticmoments,therelative
energybetweenthesestatescanbetunedbyexternalmagneticfields.Bysuitable
rampsofthesefields,populationcanbetransferredfromanatom-pairstatetoa
boundmolecularstate[Joc03,Reg03,Zwi03,D¨ur04,Ino04,Sta04].Thesemolecules
areproducedinahighly-excitedvibrationalstate.
Meanwhileithasbeenshownthatvibrationaldeexcitationcanbeachievedby
applicationofRaman-laserpairs[Dan08,Lan08,Osp08,Dan09,Osp09].Withthis
method,ultracoldhomonuclearRb2moleculeshavebeenproducedintherovibra-
tionalgroundstateofthea3Σu+electronicstate[Lan08].Thismethodisalsoap-
plicabletopolarmolecules,ashasbeendemonstratedwiththetransferofultra-
coldKRbtotherovibrationalgroundstateofthea3ΣandX1Σelectronicstates
[Ni08,Osp09,Ni09].Unfortunately,thevarietyofmolecularspeciesobtainableby
thistechniqueislimited:themoleculesareforgedtogetherfromatomswhichcanbe
efficientlylasercooledandtrapped,essentiallylimitingthistechniquetohomonu-
clearandheteronuclearalkalidimers.

Photoassociationproducesmoleculesviaopticalexcitationofanelectronically
excitedmolecularstateduringthecollisionoftwoground-stateatomsinadenseand
coldatomiccloud[Let93,Mil93,Abr95,Wan96,Fio98,Pil00].Theexcitedmolec-
ularstatemaythenspontaneouslydecay–orbetransferreddownbylaserfields–to
rovibrationalstateswithintheelectronicground-statemanifold.Startingwitha
two-speciescloudofultracoldatoms,polarmoleculessuchasKRb,NaCs,RbCs,or
LiCscanbecreatedbyphotoassociationaswell[Hai04,Ker04a,Ker04b,Man04,
Wan04,Kra06].However,thesemoleculesproducedbyphotoassociationtypically
populatemanydifferentrovibrationalstatessincethemoleculesspontaneouslydecay
state.groundelectronicthetoToarriveatacoldmolecularsampleinasinglerovibrationalstate,alaser-
stimulatedtransferschemecanbeemployed[Sag05].Choosingasuitablerovi-
brationalstateintheelectronicallyexcitedstatewithfavorableFranck-Condon

8

moleculesolarpCold

factors,alsospontaneousdecaycanleadtoefficientdecayofmoleculesintothe
rovibrationalgroundstate[Dei08b].Thepopulationofrovibrationalstatescanalso
beredistributedbyexcitationwithbroad-bandwidthpulses.Usingasuitablehigh-
frequencycutoff,suchthattherovibrationalgroundstateisnotresonantlyexcited
anymore,populationtransfertotherovibrationalgroundstateisachieved[Vit08].
Replacingthesharpfrequencycutoffbypulse-shapingtechniques,evenpopulation
transfertoanarbitraryselectedvibrationallevelispossible[Sof09].Sincephotoas-
sociationdemandsfordensecloudsofultracoldatomstobeginwith,themolecular
specieswhichcanbeproducedbyphotoassociationarelimitedtoalkalidimers,same
asfortheFeshbachmolecules.

1.2.2Directmethods:Controllingtranslationalandinter-
motionmolecularnaltoproBuffer-gasducecocoldpolingolarinamoleculescryogenicinenthegasvironmenphasetw[asWtheei98].firstsucceMoleculesssfulintheapproacgash
allyphaseandareinloadedternallyinbytothecollisionsbuffer-gaswiththecell,coldandheliumthenatoms.thermalizeSevberalothmethotranslatiodsaren-
availabletobringthemoleculesintothebuffer-gascell.Thegas-phasemolecu-
les,inthiscaseCaH,canbeproducedintheheliumbuffergascellbylaserab-
lationfromasolidtarget,hereCaH2.Analternativetolaserablation,increasing
theflexibilityconcerningtheavailablemolecularspecies,isloadingfromabeam
[Ego02,Ego04]orawarmcapillary[Pat07,Som09,vB09].Afterbeingcooledby
collisionswiththecoldheliumatoms,themoleculescanbemagneticallytrapped
bytrappedincludingsampleaofsuitablemoleculesallomagnetic-field-coilws,e.g.,studiesarrangemenofcollisiontintheandcryrelaxationogenicsetup.processesThe
[Cam07,Cam08,Hum08b,Cam09].
Buffer-gascoolingcanalsoserveasasourceforcoldmolecularbeams[Max05].
Here,themoleculesthermalizebycollisionswiththecoldheliumbuffergas,before
theyleavethecryogenicenvironmentthroughanexitholeinthebuffer-gascell,
formingamolecularbeam.Thisextractionofcoldmoleculesfromthebuffer-gascell
canbecombinedeitherwithamagnetic[Pat07]oranelectric[Som09,Pat09,vB09]
expguide,erimenwhicts.hAdvdelivanerstagestheofthemoleculesbutoffer-gas-coanolingultrahigh-vtechniqueacuumarechamtheberhighforfluxesfurtherof
species.moleculesThewhicachhiearevacablehievtempableeandraturetheisflexibilitessenytiallywithrespdeterminedecttobythetheusedrefrigeratormolecular
usedtocooltheheliumbuffer-gascellandbytherequirementofasufficientlyhigh
heliumdensityforefficientcooling.

andStarkfoandcussingofZeemanchargeddecelerationparticlebeamsapplytoinfluenceconceptsthedevelopmotionedofforptheolaraccelerationmolecules.
isToconreplacedtrolabpyolartheforcemolecule’sduetomothetion,intheteractionCoulomofbaforcedipoleactingwithonanachargedinhomogeneparticleous

1.2Productionofcoldpolarmolecules

9

electricormagneticfield[vdM08].Allthesedecelerationexperimentsemploya
supersonic-expansionmoleculesource[Pau00].Insuchasource,thetemperatureof
thebeamcanbeaslowasafewKinthecomovingframe.Additionally,theinternal
degreesoffreedomarecooleddowntolowtemperatures(≈1–10Kforrotations,tens
ofKforvibrations).Thiscoolinghappens,however,atthecostofahighcenter-
of-massvelocityofthemolecularbeamwhichis,dependingontheusedcarriergas,
intherangeofafewhundredm/s.StarkandZeemandecelerationnowaimat
bringingthesefastmolecularbeamstoarestinthelaboratoryframe.
Byswitchingaseriesofhigh-voltageelectrodesonandoffinadedicatedtiming
sequence,asituationcanbeestablishedinwhichthemoleculeloosesitskinetic
energyonitswayalongthedecelerator[Bet99,Bet02].Furthermore,alsotrans-
versefocussingandtransversestabilityisguaranteedforthemoleculesmovingsyn-
chronouslywiththeswitchingoftheelectrodes.Theslowed-downmoleculescan
thenbeloadedintoanelectrictrap[Bet00,Bet06],intoastoragering[Cro01]ora
molecularsynchrotron[Hei06,Hei07].Avarietyofexperimentscanbeperformed
withthesedeceleratedandtrappedmolecules.Theseinclude,e.g.,thelifetime
measurementoftheexcited3aΠstateinmetastableCO[Gil07],studiesofopti-
calpumpingbythethermalblackbodyradiationfortrappedOHandODradicals
[Hoe07],ortheobservationofcoldcollisionsbetweendeceleratedOHmoleculesand
asupersonicbeamofXeatoms[Gil06].
WhileaconventionalStarkdeceleratorisabigmachines,typicallyconsisting
ofhundredsofelectrodeswhichresultsinatotallengthexceeding1m,itwasre-
centlyshownthatmicrofabricationallowsforadramaticminiaturization.Since
largeelectric-fieldgradientscanbeachievedwithsuchstructures,guidingandde-
celerationofpolarmoleculesispossibleincompactsetups.Forexample,atotal
lengthofonly5cmwasneededtodeceleratemetastableCOmoleculesfrom312m/s
to96m/s[Mee08,Mee09].Theneedforlongdecelerationdistancesinamulti-stage
Starkdecelerator,relyingonsubsequentswitchingofhigh-voltageelectrodes,canbe
circumventedaswellbyexploitingthehugeelectricfieldsreachedinthelightpulses
producedbyamode-lockedlaser[Sie86].Focussingsuchpowerfullaserpulses,the
largeelectricfieldgradientswhicharenecessarytoinfluencethemotionofpolarmo-
leculescanbeachieved[Sta97,Cor99,Bar01,Bar02,Don05].Thiswasexperimen-
tallyusedtodeceleratepulsedatomicandmolecularbeams[Ful04,Ful06a,Ful06b].
Itshouldbementionedthatnotonlydecelerationwithpulsedelectricfields,
i.e.,Starkdeceleration,isusedtoproducecoldmolecules,butotherdeceleration
schemesexistaswell.Pulsedmagneticfieldsareusedtoslowdownparamagnetic
atomic[Nar07b,Nar07c,Van07,Hog08a,Nar08a,Rai09]andmolecular[Nar08b]
beams.Hydrogenatoms,whichhadbeenslowedbysuchaZeemandecelerator,
weresuccessfullyloadedintoamagneticquadrupoletrap[Hog08b].
OneimportantfeatureofStarkandZeemandecelerationisthetunabilityofthe
finalvelocityofthemolecules.Thisoffersasimplemannerforadjustingtherelative
energyinacollisionexperiment,whichwas,e.g.,successfullyusedinthestudyof
thecollisionXe+OHintheexperimentbyJ.J.Gilijamseetal.[Gil06].

10

molecolarpColdules

Mechanicalmethodshavebeenemployedaswelltoproducecoldmolecules.
AsinaStarkdecelerator,theseexperimentsstartwithcoldbutfastmolecular
beamsproducedinasupersonic-expansionsourceandtrytobringthesebeamstoa
standstillinthelaboratoryframe.Possibleconfigurationsaremountingthenozzle
ofasupersonicexpansiononaspinningrotor[Gup99,Gup01],billiard-likecollisions
betweenNOmoleculesandAr[Eli03],andreflectionsofthemolecularbeamfrom
cleansiliconsurfacesmountedonarapidly-rotatingpaddle[Nar07a].

Reachinglowertemperatureswithmoleculesproducedbydirectmeansre-
mainschallenging.TypicaltemperaturesachievableinthelaboratorybyStarkde-
celerationorbuffer-gascoolingareinthe10mKrange.Cavitycoolingisoneofthe
thepropcoldosedtoscthehemes[ultracoldHor97,Vregimeul00,Vwithul01,Lev08molecular,Wal08samples.,Sal09In]toconbridgetrasttothegapfree-spacefrom
molaserde,cosupoling,ersespdingonthetaneousneedforemissionclosediscycreplacedlingbytransitionscoherentandscatteringmakingincatovitythecocaoling,vity
inprinciple,applicabletomolecules.Inacoupledatom-cavitysystem,thecoolingis
achievfrequencyedbyofchotheosingcavity.suitableCavitycodetuningsolingb[etwMur06aeen,theMur06bpump]wlaserasandthedemonstratedresonanforce
timesatomicofthesystemsatoms[Bla03in,theCha03cavit,yMau04mode.,ThisNuß05ap,ermittedNuß05b]toandpalloerformwedverylongerchallengingstorage
anddifficultexperimentssuchas,e.g.,theobservationofthenormal-modesplitting
inastronglycoupledatom-cavitysystem[Mau05b,Mau05a],therealizationofa
deterministicsingle-photonserver[Hij07a,Hij07b],andthedemonstrationofatom-
photonentanglementinanatom-cavitysystem[Web08,Web09].Bysurrounding
anstratedion[trapLei09with].Inantheopticalresolvcaedvity,casidebandvitycoregime,olingoftheasinglevibrationaltrappedquaniontumwasnumdemon-ber,
correspondingtothemotionalstateoftheioninthetrap,isloweredbydetun-
ingthecavitywithrespecttotheexcitinglaser.Thesteady-statetemperatureis
thendeterminedbythecompetitionbetweenphoton-recoilheatingduetoscatter-
ofingcainvittoyfreecoolingspacecanandbecoolingextendedbytoscatteringincludealsophotonstheintocomplexthecainvityternal.Thestructutheoryre
ofwithrespmolecules.ecttoBymolecularappropriatetransitiontuningfreofthequencies,pumprotationallaserancodolingthecaofvitymoleculesfrequencyvia
cavity-stimulatedtransitionsshouldbepossible[Kow07,Mor07].
Single-photoncooling[Pri08]oropto-electricalcooling[Zep09]areother
schemesthatintendtocoolmoleculesbyquantum-opticalmethods.Incontrastto
momenstandardtumlasertocotheoling,atomandwheremothedifysmallitsphotonmotionalrecoilstate,istheseusedsctohemesiterativuseelythetranspsofen-r
taneousdecayfollowingopticalexcitationonlyasameantoremoveentropy.Kinetic
energyisremovedbyexploitingthemodifiedinteractionenergywithexternalfields
whenthemoleculeistransferredtoadifferentinternalstate.Sincetheinteraction
derenergyof1ofK,ponlyolarasmallmoleculesnumwithberanofexternallyphoton-scatappliedteringevenelectrictsisfieldnecessarycanbetooncotheolother-

1.3ApproachoftheRempegrouptoproducecoldmolecules

11

moleculesbyasubstantialamount.Thisremovestheneedforfastdecayratesand
highly-closedcyclingtransitionsimposedbystandardlasercooling,makingsuch
schemesanattractivenewapproachforawideclassofpolarmolecules.

1.3ApproachoftheRempegrouptoproduce
coldmolecules:Electricvelocityfilteringand
guidingIntheRempegroup,adirectmethodfortheproductionofcoldpolarmoleculeshas
beendeveloped.Itisbasedontheconceptthatanyroom-temperaturegascontains
slow–andthereforecold–molecules;theyonlyneedtobefilteredoutinanefficient
way.ThisisaccomplishedbyexploitingtheStarkeffect,whichapolarmoleculeex-
periencesinanelectricfield.Anelectricdipoleplacedinaninhomogeneouselectric
fieldexperiencesaforce,thedirectionoftheforcedependingontheorientationof
thedipolewithrespecttothefielddirection.Inaquantum-mechanicaldescription
theorientationoftheclassicaldipoleisreplacedbytheexpectationvalueforthe
projectionofthedipolemomentonthefieldaxis.Thisgivesrisetothedependence
oftheStarkshiftontherotationalstateofthemolecule.Amoleculecanhence
beinalow-field-seeking(lfs)orhigh-field-seeking(hfs)state.Inthisthesis,only
theproductionofbeamsofpolarmoleculesinlow-field-seekingstates,whichcan
beguidedinelectrostaticfields,isconsidered.Theelectricfieldscreatedbyhigh-
voltageelectrodesconnectedinaquadrupolarmannerallowtrappingoftransversely
slowmolecules.Selectiononthelongitudinalvelocityisobtainedbybendingthe
guide.Theselectedslowpolarmoleculescanthenbeguidedalonglargedistances
toaseparateultrahigh-vacuumchamber[Ran03,Jun04a],wheretheyareavailable
forfurtherexperiments[Rie05].However,itshouldbenotedthatalsomoleculesin
high-field-seekingstatescanbeguidedusingtimevaryingfields[Jun04b].

1.3.1History,developments,andextensionsoftheelectric
guideVelocityfilteringusinganelectrostaticquadrupoleguidewasfirstdemonstratedwith
formaldehyde(H2CO)anddeuteratedammonia(ND3)molecules[Ran03,Jun04a].
There,fluxesof1010–1011molecules/satpeakdensitiesof109cm−3wereachieved
usingtypicallaboratoryguidingfieldsof100kV/cm.Themoleculesintheseguided
beamshadvelocitiesofaround50m/s,correspondingtoatranslationaltemperature
ofafewKelvin.Sincestaticelectricfieldswereusedintheseexperiments,only
moleculesinlow-field-seekingstatescouldbeguided.
Toextendthevelocity-filteringtechniquetomoleculesinhigh-field-seekingstates,
adynamicaltrappingpotentialmustbecreated.Thisisaccomplishedbyswitching
theelectricguidebetweentwodipolarconfigurationsinaperiodicmanner.Thereby,

12

ulesmolecolarpCold

moleculesinlow-field-seekingandhigh-field-seekingstatesalikecansimultaneously
betrappedinatime-averagedpotential.Intheexperimentitwasshownthatguiding
ofpolarmoleculesinsuchalternatingelectricfieldsisindeedpossible[Jun04b].
However,simulationssuggestedthatonlylow-field-seekingmoleculesreachedthe
detectionvolumeattheexitoftheguide.Toshowthathigh-fieldseekerscanbe
trappedbyalternatingfieldsaswell,anelectrictrapforneutralrubidiumatomswas
setup[Rie07b].Anothermotivationforthisexperimentwastheprospectoftrapping
atomsandmoleculessimultaneouslyinthesametraptoachieve,e.g.,sympathetic
coolingofthemolecules.Totrapthem,rubidiumatomsarepre-cooledinamagneto-
opticaltrapandthenmagneticallytransferredtotheall-electrictrap.Forthese
high-field-seekingrubidiumatomsstoragetimesofafewhundredmillisecondsin
theelectrictrapweredemonstrated.
Sincemanyexperimentsbenefitfromlonginteractiontimesofthemoleculesand,
e.g.,laserfieldsorothermolecularoratomicspeciesforthestudyofcollisions,the
electrostaticquadrupoleguidewasconnectedtoanelectrostatictrapformolecules
[Rie05].Thetrapconsistsofseveralringelectrodeswhichmatchinanaturalwayto
theelectricquadrupoleguide.Withthiscontinuously-loadabletrap,storagetimes
of130msattemperaturesof300mKweredemonstratedforammoniamolecules.
Thelifetimeofthemoleculesinthistrapislimitedbytheprobabilityoffindingan
escapechannel,givenbyeithertheexitorentrancequadrupoleguide.Thisresults
inavelocity-dependentlifetimeofmoleculesinthetrapsincefastmoleculesprobe
thesurfaceenclosingthetrapvolumemorerapidly.Thisopenstheperspectiveof
reachinglongerstoragetimesbyamoreelaboratedesignofanelectrostatictrapfor
molecules.olarpInthefirstguidingexperimentsmolecularspeciessuchasformaldehydeoram-
moniawereused.Apolarmoleculewhichisofhighinteresttodifferentfieldsiswa-
ter.However,duetoitsmolecularstructure,ordinary(H2O)andfully-deuterated
(D2O)waterexhibitsquadraticStarkshifts.Therefore,guidingandtrappingis
significantlymorechallengingthanwithformaldehydeorammoniawhichexhibit
large,linearStarkshifts.Nevertheless,withtheelectrostaticguidingandvelocity-
filteringtechniquecoldguidedbeamsofdeuteratedwater(D2O)couldbeproduced,
showingtheversatilityofthismethod[Rie06].Recently,theseexperimentswith
coldguidedwaterbeamswereextendedtoincludeallthewaterisotopologuesH2O,
D2O,andHDO[Mot09b].Althoughseemingverysimilaratafirstglance,these
moleculesshowadistinctbehaviorwhenexposedtotheguidingelectricfields.This
allowedtoinvestigatedifferentaspectsofthevelocity-filteringprocesssuchasits
dependenceonrotationalstatesofthepolarmolecules.
Thefluxofcoldguidedpolarmoleculesissohighthatitiseasilydetectedwitha
quadrupolemassspectrometer(QMS).Thishastheadditionaladvantageofbeing
robustandflexible.However,withthismeasuringtechniquenodirectinformation
onthepopulationofinternalstatesofthemoleculesisavailable.Therefore,the
detectionwiththeQMSwascombinedwithalaser-spectroscopytechnique[Mot07].
Intheguide,formaldehyde(H2CO)moleculeswereopticallypumpedtoanexcited

thesisThis1.4

13

statewhichdissociatesrapidly.Ifthisopticalpumpingisdoneinastate-dependent
way,thelaser-frequency-dependentdecreaseoftheQMSsignalallowstoinferin-
formationonpopulationsofindividualrotationalstatesoftheguidedmolecules.In
principle,thistechniqueisapplicabletootherspeciesaswellsincecouplingtoan
unguidedstateissufficienttogeneratelossesfromtheguidedpopulation.
Inallexperimentsmentionedsofarthemoleculeswereextractedfromathermal
reservoirwhichcould,atmost,becooledto150K.Thesourcewould,however,ben-
efitalotfromstartingwithanensemblealreadyatcryogenictemperatures.There-
fore,electrostaticvelocityfilteringwasrecentlycombinedwithbuffer-gascooling
[Som09,Pat09,vB09].Here,moleculesareinjectedintoacryogenicheliumbuffer
gasthroughaheatedinputcapillary.Themoleculesthermalizebycollisionswith
thecoldheliumatoms[Wei98],andfinallyleavethebuffer-gascellthroughanexit
aperture[Max05,Pat07,Som09,Pat09,vB09].Thisbeamleavingthecellisthen
collectedbytheelectricguide.Withthissetup,guidedbeamswithdensitiesof
109cm−3andfluxesof1011molecules/satvelocitiesof60m/sareproduced.Bycol-
lisionswiththecoldheliumbuffergasnotonlythetranslationaldegreesoffreedom,
butalsointernalexcitationsarecooled.Withthedepletion-spectroscopytechnique
forformaldehydeitcouldbeverifiedthattherotationaldegreesoffreedomare
cooleddowntothetemperatureofthebuffergas,4K,resultinginastate-selected
beamwithatleast80%ofthepopulationinasinglerotationalstate.

thesisThis1.4

Thisthesisfocussesonthepropertiesofcoldguidedbeamsofpolarmoleculespro-
ducedbyelectrostaticvelocityfiltering.Mainquestions,whichareaddressed,are,
howtheinternal-statedistributioninfluencesexperimentswithguidedmolecules,
howitisexperimentallyobservable,andhowitcanbealteredandcooleddown.
Inchapter2theworkingprincipleofelectrostaticvelocityfilteringandguidingis
explained,andthesetupusedfortheexperimentsispresented.Measurementswith
deuteratedammonia(ND3)moleculesarediscussed,whichshineanewlightonthe
detectionprocess.Morespecifically,thequestion“whatisactuallymeasured?”is
addressed,anissueofhighestrelevanceforcalibrationsofthefluxofguidedmole-
cules[Ran03,Jun04a,Som09,vB09].Inchapter3measurementswithdeuterated
ammonia(ND3),whichhavebeenperformedoverawiderangeofinletpressures,
arepresented.Theresultsshowthatcollisionaleffectsinthevicinityofthenozzle
mustnotbeneglected,althoughthesourceisoperatedinthenear-effusiveregime
[Mot09a].Thesecollisionsultimatelylimitthefluxofcoldmoleculesachievableby
electrostaticextractionofmoleculesfromathermalreservoir.Therefore,anopti-
mizationofthesourceforfutureexperimentsrequiresprofoundknowledgeofthese
effects.Inchapter4guidingexperimentsperformedwiththedifferentwateriso-
topologsH2O,D2O,andHDOarepresented.Althoughthesemoleculesarevery
similarconcerningtheirchemicalproperties,theyshowasurprisinglydifferentbe-

14

ulesmolecolarpCold

haviorinthevelocity-filteringprocess[Mot09b].Anexplanationisfoundfromthe
theoreticalmodelofelectrostaticvelocityfilteringandguiding.Accordingtothis
model,theguidingefficiencyessentiallydependsonafavorableStarkshift.These
molecularStarkshiftsarerelatedtotherotationallevelstructureandsymmetry
propertiesoftheconsideredmolecules.Sincetheindividualwaterisotopologshave
aspecificrotationalenergy-levelstructure,thesedifferencesintheirguidingefficien-
cieshintattheimportanceoftheinternal-statedistributionforaproperdescription
ofthevelocity-filteringprocess.Depletionspectroscopyofformaldehyde,whichis
presentedinchapter5,providesdirectaccesstotheinternal-statedistributionof
moleculesintheguidedbeam.Toaddressindividualrotationalstates,adetailed
understandingoftheformaldehydespectrumisnecessary.Withmolecularconstants
obtainedfromtheanalysisofroom-temperatureabsorptionspectra,assignmentof
theobservedtransitionstorotationalstatesispossible.Sinceformaldehydemole-
culesdissociatefollowingultravioletexcitation,alossofmoleculesfromtheguided
beam,i.e.,adepletioninthedetectorsignal,isinduced.Thisdepletionisamea-
sureforthepopulationoftheaddressedinternalstateandisusedtocharacterizethe
internal-statedistributionintheguidedbeam.Inchapter6theenhancementof
Rayleighscatteringbyanopticalcavityisdiscussed[Mot09c].Suchcavity-enhanced
lightscatteringmightbeusedasanon-destructivedetectionschemeforultracold
molecules.Theresultsofthisthesisworkopennewroadsforfutureexperiments
withcoldpolarmolecules,whichareillustratedintheoutlookgiveninchapter7.

2Chapter

guidingElectrostaticofpolarvelocitymoleculesfilteringand

Inforthe195high-precision0’s,Zacsphariasectroscopetal.ybymadedirectingeffortsantoproeffusivduceebsloeamwupatomswardsandinamoleculeskindof
fountain[Zac54,Ram90].Theslowmoleculeswereexpectedtoreversetheirtravel
heighdirectiont,sucinhthethatgratheyvitationalcouldbefieldofdetectedtheatEarththebasealreadyoftheafterfounascendingtain.Hoawevsmaller,
noslowmoleculescouldbeobserved.Theexplanationforthisistwofold:First
ofall,afterleavingtheeffusivesource,thebeamdilutesbyspreadingout,sothat
wtheayup,densitytheofslorevwersedmoleculesmoleculesarepatermanenthetlydetectorbomisvbardederybysmall.fastSecond,moleculesonfromtheir
behind.Inthesecollisionstheslowmoleculesgainsomuchenergyandmomentum
inforwarddirectionthatfinallythenumberofslowmoleculesissolowthatnone
detected.ebcanNotwithstandingtheexperienceswiththeZachariasfountain,itispossibleto
obtainmoleculesslowfromanmoleculeseffusivbyevelosourcecitycanbfiltering.eimproThevedfilteringdecisivelybefficiencyyanumofbtheerofslowmea-est
sures.Oneis,ofcourse,improvedtechnologyintermsofbetterdetectorsanda
betterspreadingvacuum.transvBut,erselybmoreyanimportanappropriatetly,itisguidingcrucialtostructure.preventThisthecanbmoleculeseachievfromed
withamagneticguideforparamagneticatomsandmoleculeswhichpossessunpaired
electrons[Gha99,Pat07].Forpolarmolecules,whichpossessapermanentelectric
dipolemoment,electricguidesarebettersuited.Aschematicrepresentationofan
experimentalsetupforvelocityfilteringbysuchanelectricguideisshowninFig.2.1.
Byprovidinganelectricfieldwhichincreasesinalltransversedirections,molecules
intheirlotransvw-field-seekingersevelocitstates,yisi.e.,smallthoseenough.withaMoreopvositiver,eabStarkendinshift,thewillguidebeoffersguidedtwoif
additionaladvantages:First,thelongitudinalvelocityisalsolimited,sincethecen-
iftriptheiretalforcelongitudinalsuppliedvelobycittheyiselectricsmallfieldenough.onlySecond,guidesabmoleculesendinthearoundguidetheextraccornerts

15

16

Electrostaticvelocityfilteringandguidingofpolarmolecules

Figure2.1:Schematicoftheelectrostaticvelocity-filteringandguidingexperiment.Mo-
leculesleavetheeffusivesourcethroughtheexitholeandarefunneledintotheelectric
quadrupoleguide.Theguidingelectricfieldsprovideatwo-dimensionaltrappingpoten-
tialfortransverselyslowmolecules,whereasfilteringonlongitudinalvelocityisachieved
bybendingtheguide.Theslow,andhencecold,moleculesareguidedthroughdifferen-
tialpumpingstagestoanultrahigh-vacuumregion,wheretheyareavailableforfurther
ts.erimenexp

theslowmoleculesfromtheregionwherecollisionswithfastmoleculesfrombehind
aremostlikely.Themoleculesarebroughtrapidlyintoanultrahigh-vacuumregion,
wherecollisionsarerare.Theseguidingideasweresuccessfullyimplementedinthe
Rempegroupinthepastyearstocreatehigh-fluxbeamsofslowpolarmolecules
[Ran03,Jun04a,Rie06,Mot09a,Mot09b].

2.1Theoryofelectrostaticvelocityfilteringofpo-
moleculeslarVelocityfilteringofpolarmoleculesisbasedonselectionoftheslowestmolecules
slofromwamoleculesthermalleagas,vingasscaneffusivhematicallyesourceshownininanFig.efficien2.2.twAnaybyelectricaccepguidetingacollectslarge
thesolidrelativangle.efractionAlthough,ofsloaccowrdingmoleculestothewithMaxwenergiesell-Boltzmannbelow1vKeloiscityonly10−4distribution,fora
quitethermalhigh,gaswheatnroomstartingtempwitherature,sufficienthetlyabsolutehighgasdensitdensityyof.slowmoleculescanbe
TheUsingguidingsuitableandtrappingelectric-fieldpotentialgradienforts,slowforcescanmoleculesbeisexertedrealizedoninptheolarformmolecules.ofan
fieldselectricachievquadrupableoleinthefield,labwhichoratoryisarecreatedonbythefourorderhigh-vof100oltagekV/cm.electroTdes.hisresultsElectricalin
trapdepthsontheorderofaKelvinfortypicalmolecularStarkshiftsof≈1cm−1
atwithinthesethefields.regionTransvenclosederselybyslohighwelectricmoleculesfields,inlowhereasw-field-seekingfastmoleculesstatesareescaptrappetheed

2.1Theoryofelectrostaticvelocityfilteringofpolarmolecules

17

Figure2.2:Ideaofelectrostaticvelocityfiltering.(a)−4Thermalvelocitydistributionof
ammonia(ND3)molecules.Aconsiderablefraction,10,ofthemoleculeshasavelocity
below≈35m/s,correspondingto1K.(b)Electric-fielddistributioninthequadrupole
guidesurroundedfor±b5ykVfieldselectrorisingdevtoatoltage.leastIn93thekV/cmcenterinallandirections.electric-field(c)minimStarkumenergyisofformed,an
electricdipole.Dependingontheorientationoftheelectricdipolemomentdwithrespect
totheexternalelectricfieldE,themoleculewillminimizeitsenergyatsmallelectricfields
(lotrappw-fieldedandseekers,guidedlfs)inorahighquadrupelectricolepotenfields,tialrespsuchectivaselthey.oneMoleculesshownininlfs(b).statescanbe

18

Electrostaticvelocityfilteringandguidingofpolarmolecules

theguide.centrifugalFilteringforceonexceelongitudinaldsthevelorestoringcityisforceachievofedthebybguidingendingquadruptheoleguide.field,Whenthe
fastmoleculescannotfollowtheguideandarelost.
Thetotalfluxofguidedmoleculescanbecalculatedfromthenumberofmolecules
inenergythesotoburceetrappwhichedareinintheapotenguidabletialincreatedternalsbtyatetheandelectricwhichhafields.veaInthesufficienfollotlywinlog,w
thisfixedfluxStarkofshift.guidedThemoleculesextensionistoacalculatedvarietforyofjuststatesoneinisthenternaldiscussedmolecularincstatehapterwith4a.

2.1.1Velocitydistributionsinthethermalsource
Beforecalculatingthefluxofguidedmolecules,thevelocitydistributionsofmole-
culesTheseinarethegiventhermalbyareservoir,three-dimensionalfromwhich(3D)theyMaxwareextracted,ell-Boltzmannmustvelobecityconsidered.distribu-
tionf3D(v)dv=√43v2exp(−v2/α2)dv(2.1a)
απandbyaone-dimensional(1D)velocitydistribution
f1D(vx,y,z)dvx,y,z=√1παexp(−v2x,y,z/α2)dvx,y,z(2.1b)
andwithtotalmostvelociprobabletyv=velovcitx2y+αvy2=+vz2.2kBT/m,velocitycomponentsvi(i=x,y,z)
2.1.2Cutoffvelocitiesintheelectricguide
Aswasalreadydescribedqualitativelyintheintroductiontothissection,theflux
ofwithguidevelodcitiesmoleculesbelowisgivcertainenbytransvtheersepartandofthelongitudinalmoleculescutoffinjectedvelointocities.theTheseguide
thecutoffpropveloertiescitiesofdeptheendguide.ontheTheStarkmaximalshiftoftransvtheersevmolecules,elocityvtheirmax=mass2Δm,Wsand/monis
sfieldEdeterminedmax.IfbythetheSttransvarkerseshiftveloΔWcity(vE⊥max=)reacvx2+hedvy2atofthethemaximmoleculeumofexceedsthevmaxtrapping,it
islostfromtheguide.Themaximallongitudinalvelocityvl,maxcanbeobtainedby
equatingthecentrifugalforceinthebendofradiusRandtherestoringforceofthe
guide,resultinginvl,max=ΔWs(Emax)R/rm=R/2rvmax.Here,risthefree
Ininnertheradiususedofsetup,thetheguide,atdiameterwhichthetheguide’smaximumelectroofdestheistra2mm,ppingandfieldtheisreacdistancehed.
betweenneighboringelectrodesis1mm.Thisresultsinr=1.12mm.Asalmost
everycomparedparticletofilisteringguidedby,ifve.g.,l<vl,rotatmaxingandfilterv⊥<vwheelsmax,andthisapyieldsertures.higherefficienciesas

2.2Experimentalsetup

19

moleculesguidedofFlux2.1.3Tocalculatethefluxofguidedmolecules,thevelocitydistributionsofmolecules
enteringtheguidefromaneffusivesourceareintegratedtothecutoffvelocities.In
thelimitofsmallcutoffvelocitiesvmaxandvl,maxcomparedtothethermalvelocity
α,theexponentialexp(−v2/α2)inthethermalvelocitydistributionsEq.(2.1)can
bereplacedby1.Then,thefluxΦofguidedmoleculesinamolecularstatewitha
StarkenergyΔWsisgivenby
vmaxvmaxvl,max
Φ=f1D(vx)f1D(vy)vzf1D(vz)dvxdvydvz(2.2)
vx=−vmaxvy=−vmaxvz=0
∝v4max∝(ΔWs)2,
wherethedependenceofthetransversevelocityonthelongitudinalcutoffvelocity
isneglected,andΦisnormalizedtothefluxofmoleculesoutofthenozzle.The
guidedfluxcanhencebedescribedbyafunctionfwhichgivesthefractionof
guidablemoleculesforagivenelectricfield,Φ=f(ΔWs)∝(ΔWs)2.
setuptalerimenExp2.2Thesetupusedfortheexperimentspresentedinthisthesisisalreadydescribedin
[Mot09a,Mot09b].Manypartsofthesetup,especiallythequadrupoleguide,are
similartooradoptedfromtheonesusedintheRempegroupforpreviousexperi-
mentsanddescribedinthethesisofTobiasJunglen[Jun05].Thequadrupoleguide
forpolarmoleculesislocatedinthreeinterconnectedultrahigh-vacuumchambers,as
shownschematicallyinFig.2.3.Theguideconsistoffourstainless-steelelectrodes
withadiameterof2mm,whicharearrangedinaquadrupoleconfiguration.The
individualelectrodesareclampedtoaceramicinsulatormount,whichalsomain-
tainsaspacingbetweenadjacentelectrodesof1mm.Applyingvoltagesof±5kV
resultsinanelectricfieldminimuminthecentersurroundedbytrappingelectric
fieldsexceeding93kV/cminalldirections.
Moleculesarecontinuouslyinjectedintotheguidethroughaceramictube(∅
1.5mm,length9.5mm)whichisconnectedtoaliquid-nitrogenreservoirandequipped
withaheaterelement,suchthatitstemperaturecanbeadjustedintherange100–
400K.Toensurethermalization,theTeflontubeforthemoleculargaspassesame-
anderingcoolingstageof≈0.3mlengthbeforeenteringtheceramictube.Through
therestofthisthesisthisceramictubewiththeattachedcoolingstage,whichis
schematicallyshowninFig.2.4(a),isshortlycalled“nozzle”.Figure2.4(b)shows
thegas-handlingsystemusedtosupplythemoleculargastothenozzle.Bycool-
ingthenozzle,thefractionofslowmoleculesincreases,astheMaxwell-Boltzmann
velocitydistributiongetscompressedandshiftedtolowervelocities.Thisincreases
theguidedflux.Furthermore,thenumberofthermallyoccupiedstatesisreduced,

20

Electrostaticvelocityfilteringandguidingofpolarmolecules

Figure2.3:Experimentalsetup.Moleculesfromthethermalreservoirentertheelectric
guidethroughtheceramicnozzle.Slowmoleculesaretrappedinthequadrupolefield
andguidedthroughtwodifferentialpumpingstagestoanultrahigh-vacuumchamber,
wheretheyaredetectedbythequadrupolemassspectrometer(QMS).Theinsetshows
theelectric-fielddistributionofthequadrupoleguidefor±5kVelectrodevoltage,resulting
inatrappingelectricfieldexceeding93kV/cm.

leadingtoanimprovedpurityoftheguidedbeamasshownbydepletionspec-
troscopy[Mot07].Thenozzleislocatedinavacuumchamber,inwhichabase
pressureof10−9mbarisachievedbya500l/sturbomolecularpump(TMP).When
flowinggas,thepressureinthechamberrisestoatypicalvalueofafew10−7mbar.
Fromthispressureriseandtheknownpumpingspeedthegasflowratethroughthe
nozzlecanbedetermined.Foratypicalreservoirpressureof0.1mbar,whichisused
formanyexperiments,thegasflowratethroughthenozzleis1×10−4mbar∙l/s.
Comparedtopreviousexperiments,whereabendradiusof25mm[Ran03,Jun04a]
oronly12.5mm[Rie05]wasused,thecurrentsetupemploysalargerbendradius
of50mm.Thishastheadvantageofanincreasedflux,whichisespeciallyvaluable
whenlookingforsmallsignalsas,forinstance,whenperformingexperimentsatvery
lowreservoirpressuresuchastheonesdescribedinchapter3.Theincreaseinfluxis
alsoveryvaluableformeasurementswithmoleculesexhibitingquadraticStarkshifts
suchasH2OorD2O[Mot09b],whicharediscussedinchapter4,orwhendoingdiffe-
rentialmeasurementssuchasindepletionspectroscopy[Mot07,vB09]presentedin
chapter5.Themoleculesareguidedaroundtwobendsandthroughtwodifferential
pumpingstagestoanultrahigh-vacuumchamber,wheretheyarefinallydetectedby
aquadrupolemassspectrometer(QMS,PfeifferQMG422).IntheQMS,theguided
moleculesareionizedbyelectronimpactinacross-beamgeometry.Theionsarethen
massfiltered,beforeinthefinalstagesingle-ioncountingusingasecondary-electron

2.3Velocity-filteringexperiments

21

Figure2.4:Gas-inletsystem.(a)Nozzleassembly.TheTeflontube,throughwhich
themoleculesarebroughttotheceramicnozzle,meandersinthecoppercoolingstagefor
thermalizationofthemoleculargas.Thetemperatureofthecopperblockiscontrolled
bybalancingthecurrentthroughtheheatingwirewiththethermallinktotheliquid-
nitrogenreservoir.Intheexperiments,temperaturesintherange150–300Kareused.To
maintainareasonablemoleculefluxoutofthenozzle,asufficientlyhighgaspressureis
necessary.Thislimitsthelowestoperabletemperaturebythetemperaturedependence
ofthevaporpressure.(b)Gasfromanammonia(ND3)bottleissuppliedtothenoz-
zle.Thegas-handlingsystem,consistingofstainless-steeltubes,isevacuatedwiththe
TurboCubetoapressurebelow10−4mbarbeforethemoleculargasesareintroduced.A:
Thermoelectrically-controlledflowvalve.B:Pressuregauges(PiraniandMembrane).C:
In-linevalve,separatingtheUHVfeedthroughfromthegas-handlingsystem.

m0–5VultiplierTTLisppulses,erformed.passedThethroughelectronicanisolatingsignalsareamplifieramplifiedtoav,oidshapgroundedtoloops,standardand
aremoleculesfinallybyrecordedtheQMSusingisanotmulticsensitivhaneneltoscalartheincard.ternalThisstates.detectionHowevofer,thebyguidedcom-
binationwithultravioletlaserspectroscopyintheguide,state-sensitivedetection
tocaninbteacernal-statehieved[Mot07diagnostics].Theinacoldpplicationguidedofbthiseamsofdepletion-formaldehspydeectroscopisytecdiscussedhniquein
.5hapterc

2.3Velocity-filteringexperiments

ofThetime-of-flighelectrostatict(TveloOF)city-filteringmeasuremenandts.guidingHere,theexphigherimenvtsoltagearep(HV)erforapmedpliedasatoserithees
electrodes,whichproducestheguidingquadrupolefield,isswitchedonandoffin
awithfixedthetimingQMS.Thesequence.signalofFigureguided2.5showsmoleculesatisypicaldeterminedtime-resolvfromedthesignaldifferencemeasuredin
thewhichpsteady-stateermitssubtraQMSctingsignaconltwithributionsHVofappliedbactokgroundthegasguidetoandtheHVQMSswitcsignal.hedoff,

22

Electrostaticvelocityfilteringandguidingofpolarmolecules

Figure2.5:Time-resolvedQMSsignal.Afterapplyinghighvoltage(HV)totheguide’s
densitelectroydesof(atguidedt=50ms),ammoniathe(NDsignal3)risesmoleculesandfinallyarrivingreacatthehesaQMSsteady-stateionizationvvalue.olumeTheis
proportionaltothissteady-statevalue.

Figure2.6allowsacloserlookattherisingedgeofthetime-resolvedQMSsig-
firstnal.Infeaturethistofigure,observeismeasuremethedneptsforendencedifferenofttheelectrodesteady-statevoltagesvalueareonthecompared.electroThede
varrivingoltage.atThistheQMSsteady-stateionizationvalueisvolume,propasortionalwilltobetheshowndensitinyofsectionguided2.4.Inmoleculessec-
tion2.1itwasexplainedthatthefluxandhencealsothedensityoftheguided
moleculesincreaseswiththetrapdepthprovidedbytheguide,i.e.,withtheelec-
troallodewsvinsigholtage.tinAtodettheaileddependenceanalysisofofthethiselectrostaticsteady-stateguidingsignalofandveloguidedcitymoleculesfiltering
onferenthetwatermolecularisotoppropologserties,incashapteris4.discussedAsalatersecondoncusingharacteristic,theexamplethearrivofalthetimedif-
ofthemoleculescanbeconsidered.Afterswitchingontheguidingelectricfields,
itarrivtake.esThaiswhiledelayuntilcorresptheondsQMStosignalthetimestartsofflighrising,tofi.e.,theuntilfastestthefirstmoleculesmoleculesfrom
thenozzletotheQMSdetectionvolume.Sincetheminimumtimeofflightisgiven
byobservtheed.lonForgitudinalincreasingcutoffveloelectrocityde,avodepltage,endethencetraonpthedepthappliedand,aselectroadevconsequence,oltageis
alsothelongitudinalcutoffvelocityincreases.

2.4Theflux-densitymystery

Instatictheguideprecedingwasgivsectionen.Ho2.3wevaer,shortoneinktroeyductionquestiontowasnotmeasuremenaddressedtswithsofar:theWhatelectro-is
theactuallydetectormeasureforthedbycoldtheguidedquadrupmolecoleules?massFsporauniectrometerformgas(QMS),inthermalwhichequilibriumconstitutes

2.4Theflux-densitymystery

23

Figure2.6:Time-resolvedQMSsignalfordifferentelectrodevoltages.Afterswitching
bonythesmallguidingarrows.electricThisdelafieldys(atcorrespt=0ondsms),tothetheQMtimeSofsignalflightrisesofthewithafastestdelayguidedtime,ammoniaindicated
(ND3)moleculesfromthenozzletothedetector,whichisdeterminedbythelongitudinal
ascutoffwellvaselocitthey.Finallylongitudinal,thecutoffsignalvreacelocithesya(observsteady-stateedviavthealue.arrivThealtimeofsteady-statethevfastestalue,
molecules),increaseswiththetrappingelectricfieldproducedbytheappliedelectrode
voltage,asdiscussedinsection2.1.

aquadrupolemassspectrometer,whichisnothingelsebutaresidual-gasanalyzer,
measuresthegasdensity[Wut04,dH08].Figure2.7(a)showsschematicallyhow
thebeamofcoldmoleculesleavesthequadrupoleguideandpassesthroughthe
ionizationvolumeoftheQMS.Inthisconfigurationamaximaldetectorsignalof
guidedmoleculesisobtained.However,itisapriorinotcleariftheQMSsignal
correspondstothenumberdensityofmolecules,sincethemoleculespassthrough
theionizationvolumewithapreferreddirectionandforwardvelocity.Forinstance,
avelocity-dependentsaturationoftheionizationyieldmightoccurandleadtode-
viationsfromadensitymeasurementandcouldevenresultinsignalsresemblinga
t.measuremenfluxTodistinguishwhethertheQMSsignalinthismeasurementconfigurationispro-
portionaltothedensityortheflux(orprobablysomethingdifferent)ofguided
molecules,itwouldbedesirabletohaveadetectoravailablewithanoutputsignal
proportionaltoeitherthetruefluxordensityofguidedmolecules.Opticalabsorp-
tionspectroscopywouldallowameasurementoftheopticaldensityandhenceofthe
numberdensityofguidedmolecules.However,duetothelimiteddensitiesinthe
guideascomparedtotheonesintypicalmolecular-beamspectroscopyexperiments,
thiswouldbeverychallenging.Fortunately,atruefluxmeasurementispossible
withtheQMSpositionedoutofthedirectlineofsightofthemoleculesleavingthe
guideinthedetectionchamber,aswillbeexplainedalongthefollowinglines.For
this,thesteady-statesituationinthedetectionchamberisconsidered,asshown
schematicallyinFig.2.7(b).AscanbeseenfromFig.2.6,already≈20msafter

24

Electrostaticvelocityfilteringandguidingofpolarmolecules

vFigureolumeis2.7:placedDetectiondirectlyofincoldthebguidedeamleamolecvinguthelesbyelectrictheQMS.quadrup(a)oleTheguideQMSforionizationmaximal
thedetectorbeamofsignals.guided(b)Themolecules.QMSTheionizationmoleculesvolumeleaveistheplacedguide,outtravofelthethroulineghofthesighvtacuumonto
cdensithambyer,nmolandoffinallymoleculesthermalizeinthebycdetectorollisiconshambwitheristhegivwenalls.byThethebalancesteady-statebetwneenumbtheer
signalincidenistfluxthereforeofmoleculespropΦortionalandtothethefluxpumpingofspguidedeedS.Inmolecules.thisconfigurationthedetector

switchingonhighvoltagetheelectrostaticguidedeliversaconstantfluxΦofcold
moleculesintothedetectionchamber.Thesemoleculesthermalizebycollisionswith
thewallsofthevacuumchamber.Thevacuumpumpwithaconstantvolumepump-
ingspeedSactsasadrainforthesemoleculesaccumulatinginthevacuumchamber.
Inasteadystate,thedensitynmolofmoleculesisgivenbythebalancebetweenthe
incidentfluxofguidedmoleculesintothedetectionchamberandthepumpingspeed,
nmol=Φ/S.BymovingtheQMSionizationvolumeoutofthedirectlineofsight
ontotheguidedbeam,itcanbeoperatedasaresidual-gasanalyzerwhichmonitors
theincreaseofbackgroundgasdensityduetothecoldmoleculesguidedintothe
detectionchamber.Thesemoleculescontributingtothebackgroundgashavether-
malizedbycollisionswiththewall,suchthattheirvelocitydoesnotdependonthe
velocityofthemoleculesintheguidedbeam.Instead,theirvelocitiesaredescribed
byauniformthermalvelocitydistribution.SincetheQMSmeasuresadensitynQMS
forsuchauniformgasdistribution,oneexpectstofindnQMS=nmol∝Φ,which
resultsinasignalproportionaltothefluxofguidedmoleculesintothedetection
chamber.Therefore,suchameasurementwithoutdirectexposureoftheQMSion-
izationvolumetotheguidedbeamdisplaysthesameparameterdependenceasa
fluxmeasurementperformeddirectlyintheguidedbeam.
Figure2.8comparestheelectrode-voltagedependenceoftheQMSsignalwith
directexposureoftheionizationvolumetothebeamofguidedmoleculestomea-
surementswiththeionizationvolumemovedoutofthedirectlineofsight,entitled
indirectexposure.Alldatashownarenormalizedtothemeasuredvalueat±6kV
electrodevoltage.Onanabsolutescale,however,thecountrateswithdirectexpo-

2.4

The

yflux-densit

mystery

25

Figure2.8:MeasurementswithdirectandindirectexposureoftheQMSionization
velectroolumede-vtotheoltagebeamdepenofdenceguidedoftheammoniafluxof(NDguided3)molecules.moleculesisWithmeasured.indirectTheexpsolidosurecurvthee
bisetawfiteenbaseddirectonandtheindirectmodelexpofvosureelocityexcludesfilteringthepdescribossibilitedyinofasectionflux3.3.measuremenThediffterencewhen
thedashedQMScurvioniezareationthevmoolumdel’seisdirectlypredictionsexpforosedthetodensittheybofeamtheofguidedmoleculesinmolecules.theguidedThe
beambasedonthefitvaluesobtainedfromthefluxmeasurementwithindirectexposure.

26

Electrostaticvelocityfilteringandguidingofpolarmolecules

surearelargerbyafactorontheorderof100.Acleardifferencebetweenthetwo
typesofmeasurementsisobserved.Themeasurementwiththeindirectexposure
oftheQMStotheguidedbeam,i.e.,measuringthesteady-statebackground-gas
densitycausedbytheguidedmolecules,showsthedependenceofthefluxofguided
moleculesontheelectrodevoltageasexplainedintheprecedingparagraph.Dueto
thedifferentelectrodevoltagedependencebetweendirectandindirectexposureit
canberuledoutthattheQMSsignalunderdirectexposureisproportionaltothe
molecules.guidedoffluxInsection3.3amodelwillbedevelopedfortheelectrode-voltagedependence
ofthesignalofguidedmoleculestakingintoaccountcollisionsduringthebeam-
formationprocess.ThesolidcurvesinFig.2.8arefitsofthismodeltothedata
takenwithindirectexposureoftheQMSionizationvolumetotheguidedbeam.
Here,afluxmeasurementisassumed.ToresolvethenatureoftheQMSsignalunder
directexposureoftheQMSionizationvolumetotheguidedbeamofcoldmolecules,
thismeasurementisusedasareference.Then,basedonthesefitvaluesobtained
fromthefluxmeasurementwithindirectexposure,themodelfortheelectrode-
voltagedependence√ofthedensityoftheguidedbeamisevaluated.Forthis,an
additionalfactorU∝vforthedifferencebetweenthefluxandthedensityofthe
guidedbeamisincluded,aswillbediscussedinsection3.3.Thedashedcurvesare
thepredictionsofthismodelfortheelectrode-voltagedependenceofthedensity
ofandguhenceidedthemolecules.exactpropTheertiesgoodoftheagreemenguidedt,bindepeam,endenconfirmstofthethatreservindeedoiradensitpressurey
guidedmeasuremenbeam,tisaspiserformeddoneforwhenallthetheionizatiomeasuremennvtsolumediscussedisdirectlyinthisexpthesisosedtounlessthe
stated.otherwise

2.5Velocitydistributionofguidedmolecules

Todistributionobtaincanadditionalbeinfoconstructedrmationfromonthetheguidedtime-resolbeamvedofpQMSolarsignal.molecules,Forathvatelocitpur-y
pose,thearrival-timedistributionofthemoleculesisanalyzed.Afterswitchingon
theThehighheighvtofoltagethistheQMSsteady-statesignalsignalriseswtoasausedsteady-stateforthevalue,measurasemenshotswnindiscussedFig.2.9so.
far.However,moreinformationabouttheguidedbeamcanbeobtainedfromthis
thetime-of-fligharrivalttimes(TOF)atthesignal.detector.Forthis,Forathegivveloencitytimeofttheaftermolecuswitcleshingisoncalculatedtheguidingfrom
fields,moleculeswithvelocitiesv≥d/tcontributetothesignal,wheredisthetotal
tlengthypicallyof5them/siselectricapplied.guide.ThisThen,valueaiscbinninghosenofasathesevelocompromcitiesisebwithetwaeenbinwidthresolutionof
andsufficientsignal-to-noiseratio.Inanextstep,apostselectionisappliedto
thedata.AscanbeseenfromtheTOFtraceinFig.2.9,thesignalhasalready
closelyapproachedthesteady-statevalueforlatearrivaltimes,correspondingto

2.5Velocitydistributionofguidedmolecules

27

Figure2.9:Time-of-flighttraceofguidedammonia(ND3)molecules.Afterswitchingon
thehighvoltageappliedtotheguide’selectrodesatt=0ms,thesignalrisesandfinally
reachesasteady-statevalue.Toderiveavelocitydistribution,velocity-dependentcount
ratesarecalculatedfromthearrivaltimesandbinnedwitharesolutionof5m/s(blue
points).Toavoidsystematiceffects,dataaboveagiventhresholdofthesteady-state
valuearedropped(redsquares).

lowvelocities.Thesedatamightthereforebemoreaffectedbysystematicerrors,
sinceasmalleffectonthecountratecouldalreadyleadtoabigdifferenceinthe
velocitydistribution.Toavoidsystematiceffects,allthedataaboveagiventhresh-
old,typically99%,ofthesteady-statevalue,isnotconsideredintheevaluationof
thevelocitydistribution.Theexactvalueofthisthresholdcanslightlyinfluencethe
lowest-velocitydatapoint.Tofinallyderiveavelocitydistributionastheoneshown
inFig.2.10,adiscretizeddifferentiationisappliedtothevelocity-binnedTOFtrace
(bluedatapointsinFig.2.9).
Figure2.10showsatypicalvelocitydistributionofguidedammonia(ND3)mo-
leculesconstructedfromthetime-resolvedQMSsignal.Thisdistributionreflects,
however,thevelocityofmoleculesarrivingatthedetector,whichisplaced≈2cm
behindtheexitoftheguide,andnotdirectlythevelocityoftheguidedsample.
Whenleavingtheguidingelectrodestructure,thebeamofslowmoleculesspreads
out[Jun04a,Som09].Sincethetransverseextentoftheionizationvolume(Pfeiffer
Vacuumspecifiesavolumeof≈2×2×2mm)issmallerthanthespreadofthe
moleculesatthisdistancefromtheguideexit,theprobabilitytoentertheactivevol-
umeofthedetectorincreaseswiththemolecules’velocityinforwarddirection.This
causesarisewithvelocityinthevelocitydistribution.Incontrast,foradensity
measurementperformedintheguidethevelocitydistributionwouldbeconstant
fromsmallvelocitiesuptothemaximuminthedistribution.Theslowdecrease
insteadofasharpcutoffonthehighvelocitysideiscausedbythecontributionof
severalinternalstateswithdifferentStarkshiftsandthereforedifferentcutoffve-

28

Electrostaticvelocityfilteringandguidingofpolarmolecules

Figure2.10:Velocitydistributionofguidedammonia(ND3)moleculesarrivingatthe
whicQMShcanionizationstillbevguolume.ided,isThedeterminedcutoffvbeloycitthey,bi.e.,endtheradiusveloofcittheyoftheelectrostaticfastestquadrmoleculesupole
guideandbytheStarkshiftsofthemolecularstatespopulatedintheguidedbeam.

locitiestotheguidedbeam,aswellasbythedependenceofthelongitudinalcutoff
velocityonthetransversevelocityofthemolecules[Jun04a].
Themeanvelocityoftheguidedbeaminlongitudinaldirectionisvz≈100m/s.
Thiscorrespondstoaone-dimensionaltranslationaltemperatureofTof12K,using
E=mvz2/2=kBT.Forthemoleculesintheguidethetransversevelocityis
smaller,v⊥=2r/R≈20m/sasshowninsection2.1.Usingv=vz2+v⊥2
andE=mv2/2=3/2kBTathree-dimensionaltranslationaltemperatureof8K
isobtained.Thesetemperaturesseemrelativelyhighcomparedtopreviousresults.
AsshownbyT.Riegeretal.,moleculesfromasimilarelectrostaticguidingand
velocity-filteringsetupcouldbeloadedintoanelectrostatictrapwithatrapdepth
correspondingtoatemperatureofonly300mK[Rie05].Itshould,however,be
notedthatthetemperaturesderivedaboveonlyrepresentthemeanoftheguided
moleculesample.Duetothenatureofthevelocity-filteringprocess,alsoslowerand
hencecoldermoleculesarepresentinthebeamofguidedmolecules.Additionally,
inthepresentsetuparelativelylargebendbendradiusof50mmisused,whichis
beneficialintermsoftotalfluxofguidedmoleculesforexperimentsaimingatguiding
ofmoleculeswithsmallerStarkshifts.ForspecieswithrelativelylargeStarkshifts
suchasdeuteratedammonia(ND3)orformaldehyde(H2CO)thisresultsinahigher
temperatureoftheguidedmolecules.

3Chapter

formationtheineffectsCollisionalofcoldguidedbeamsofpolar
molecules

Inthischapter,theinfluenceofthebeam-formationprocessonelectrostaticvelocity
filteringmoleculesandcanbeguidingincreasedisinvbyestigated.raisingIntheatpressureypicalofexptheerimengast,inthethefluxreservofoirguidedand
therebpressureythebeconummesbertoofohigh,moleculestheilow-vnjectedeloincittoythetailofguide.theHowevBoltzmanner,whenthedistributionreservoiris
depletedbycollisionsbetweenfastandslowmolecules.Apartfromtheconceptual
interestinrevisitingthelow-velocitytailoftheBoltzmanndistribution,thisstudy
hasoptimizedpracticalforabspenefitsecificsinceapplicationitexplainsdemanding,howtheforcoldpinstance,olarmoleculemoleculeswithsourcecanenergiesbe
broleelowandagivhowentheytrapcandepth.beTheobservedparameterintheexprange,eriminent,whicishdiscussedcollisionalineffectssectionplay3.1a.
Inpressuresectionis3.2,discussed,thedepwhicendehnceallowsofthefirstsignalconclusionsofguidedabouteffectsmoleculesofoncollisionsthereservontheoir
bfromeamthebformation.eam,Awhicmohdiselisdevdiscussedelopinedforsection3.3.collision-inducedInsectionlosses3.4ofitsloiswshownmoleculeshow
themodelcanreproducethedependenceofthesignalofguidedmoleculesonthe
shiftselectroindevevlocitoltage.yFinallydistributions,theofeffecttheofguidedcollisionsmoleculesisconfirmedpresentedbyinthesectobservion3.5ation.of

3.1Measurementsofcollisionaleffects

Forsourcethewasdescriptionassumed.oftheThisvelomeanscitthaty-filteringtheprovelocesscityinsectiodistributionn2.1,oafthepurelymoleculeseffusive
ofinjectedmoleculesintointhetheguidenoziszle.Asassumedsoontoasdirectlycollisionsreflectbetwtheeenthermalmoleculesvelocitycomeintodistributionplay,

29

30Collisionaleffectsintheformationofcoldguidedbeamsofpolarmolecules

di.e.,ofthethemeannozzlefreeO(Λ)path≈OΛ(dof),thethismoleculesconditionbisnoecomeslongercomparablefulfilled.tothedimensions
menFtsromforanvexparyingerimeninlettalpoinpressures.tofvieTherwitebisy,effectsthereforecausedinstructivbyetocollisionsperformofmoleculesmeasure-
inthenozzleorinthehigher-densityregiondirectlybehindthenozzlecanbein-
vestigated.Furthermore,suchanexperimentisalsointerestingformorepractical
reasons.Whenusingtheguideasasourceforcoldpolarmoleculesonewantsto
operatethesysteminaparameterregimewhichresultsinthemaximumfluxof
guidedmolecules.Thisoptimalvaluedependsontherequirementsofthespecific
collisionsapplication.remoWhenvingahighpredominanfluxoftlythemoleculesslowestwithvelmoleculesocitiesareofaoffewno10m/sconcern.isneeded,There-
infore,theaguide.higherreThisservcoirhangespressureifonecanisbinecterestedhosen,inresultingonlytheinaslowhigherestfluxmolecules.ofmoleculesHere,
theuseofasmallerreservoirpressuretominimizecollisionallossesseemsadvisable.
andTo2.0inmvbar,estigateasthesemeasuredbeffects,ythethePiranireservproiressurepressuregaugeisusedvariedforbetpressureween0.01regulation.mbar
mostTheseotherpressuresexpspanerimenatswidesofarrange[Mot07around,Mot09athe,reservMot09boir].pressureTomofake0.1mthesebarnumusedbersfor
comparabletootherguidingexperimentswithsimilarsetups,thegasflowrate
risethroughinthethesounozzlercecishamber.calculatedForafromreservtheoirpumpingpressurespofeed0.1andmbartheaobservgasfloedwpressrateureof
1×10−4mbar∙l/swiththenozzleassemblyatroomtemperatureisdetermined.
trometerDuetothis(QMS)largealsovvaryariationoverinalargepressure,range.counBytratesofmeasurementhetsquadrupwitholedifferenmasstspemis-ec-
sioncurrentsoftheQMSionizationunititwasassuredthattheobservedeffects
areindeedcausedbydifferencesinthemolecularfluxandnotrelatedtosaturation
oftheionizationprocessortononlinearitiesinthedetectionprocess.Alldataused
throughouttherestofchapter3weretakenwith0.10mAemissioncurrent,except
forthevelocitydistributionsmeasuredat±3kVand0.01mbarreservoirpressure.
Here,reducethetheemissionnecessarycurrentwmeasuremenastincreasedtimes.toCo0.20mAmparingtovincrelociteaseythecoundistributionstratesmea-and
thatsuredtheathigherhigherreservemissionoircurrenpressurestoffor0.20mAdifferendotesnotemissionintrocurrenducetsitsystematicwasmadeshifts.sure

3.2Pressuredependenceofvelocityfiltering

Figure3.1showsthesignalofguidedammonia(ND3)moleculesasafunctionof
reservoirpressure.Intheseplots,measurementsfordifferentelectrodevoltagesand
sourcetemperaturesarecombined.Thecurvesarefitstothedatabasedonthe
modelforthebeamformationwhichwillbepresentedinsection3.3.Themodel
reproducesverywelltheshapeofthepressuredependenceforallelectrodevoltages.

3.2

Pressure

endencedep

of

ycitelov

filtering

31

Figure3.1:Signalofguidedammonia(ND3)moleculesasafunctionofreservoirpressure,
measuredfordifferentcombinationsofelectrodevoltageandsourcetemperature.The
curvesareindividualfitstothedatausingthemodelforthebeamformationincluding
collisionsinthehigh-pressureregion,whichisdiscussedindetailinsection3.3.Thedata
ofthe±1kVmeasurementstakenatareservoirpressure≥1mbarareinfluencedbythe
riseofthebackgroundpressureinthedetectionchamber.In(a)absolutecountratesare
shown,whilein(b)thesamedataareindividuallynormalizedforeachelectrodevoltage
andsourcetemperature.Thisfacilitatesthevisualizationoftheshiftintheoptimal
pressuresettingwiththeappliedelectrodevoltage.Besides,itshowsthatthepressure
dependenceofthesignalisindependentofthesourcetemperature.

32Collisionaleffectsintheformationofcoldguidedbeamsofpolarmolecules

Figure3.1(a)showsaswellthegood3sensitivit5yofthedetectionbytheQMS(guiding
atonly±1kV)withcountratesof10–10counts/s.
ThefirstfeaturetoobservefromFig.3.1(a)isthat,startingatzeropressure,the
signalofguidedmoleculesincreaseswithreservoirpressure,reachesamaximum,and
finallydropsagain.Thisbehaviorisexpectedconsideringtheworkingprincipleof
theguidedescribedinsection2.1.Theguideacceptsmoleculesuptocertaincutoff
velocities,whichdependonthemolecules’massandtheStarkshiftattheapplied
trappingfield.Forsmallpressures,anincreaseinpressureincreasesthenumber
ofmoleculesinjectedintotheguidewhiletheeffusivecharacterofthesourceis
maintained.Incontrasttothis,forhighpressurescollisionsinthenozzleandin
theregionbehindthenozzlebecomeimportant.Thereby,theslowmoleculesare
eliminatedfromthebeam.Thisleadstoadecreaseinthemagnitudeofthesignal
ofguidedmolecules.Themaximumisreachedatapointwherethesetwoeffects
arebalanced:Althoughmoremoleculesareinjectedintotheguide,thenumberof
moleculeswithguidablevelocitiesstaysconstantduetothereducedfractionofslow
molecules.ItshouldbenotedthatsimilarlosseswereobservedbyM.Guptaand
D.Herschbachforbeamsofcoldmoleculesaswell.Intheirexperiment,thecold
moleculeswereproducedinasupersonicexpansionfromacounterrotatingnozzle,
andthelossofslowmoleculeswasdescribedbyanattenuationfactortoaccountfor
collisionswithabackgroundgas[Gup99,Gup01].
Asecondfeaturetoobserveistheincreaseofthesignalofguidedmoleculeswith
appliedelectrodevoltage[Ran03,Jun04a,Mot09b].Asshowninsection2.1,the
cutoffvelocitiesgetlargerwhentheelectrodevoltageisraised.Forfixedreservoir
pressure,thisincreasesthefractionofmoleculeswithguidableenergies.Thede-
pendenceofthesignalofguidedmoleculesontheappliedelectrodevoltagewillbe
discussedinmoredetailinsection3.4,sinceitallowstoinfermanydetailsofthe
beamformation.Comparingmeasurementsforfixedelectrodevoltage,itcanbe
seenthatcoolingofthenozzlefrom300Kto200Kincreasesthesignalofguided
moleculesbyafactorof2.2[Jun04a].
Figure3.1(b)showsthenormalizedsignalofguidedmoleculesasafunction
ofreservoirpressure.Thisfigureallowstomaximizethefluxfromtheelectric
guideatagivenelectrodevoltage.Bychoosingtheoptimalpressuresetting,the
numberofguidedmoleculesforagivenelectrodevoltage,i.e.,uptoacertaincutoff
velocity,ismaximized.Fromthisfigureitcanalsobeseenmoreclearlythatthe
maximumofthecurveshiftstowardslargerpressureswhenhigherelectrodevoltages
areused.Thisallowstoinferthemainfeatureofthemodelusedtodescribethe
beamformation.Forhigherelectrodevoltages,fastermoleculescanbeguided.
Theincreaseoftheoptimalpressurewithappliedelectrodevoltageshowsthatfor
fastermoleculescollisionsstartplayingaroleonlyathigherpressuresandthereby
higherdensities.Thissuggeststhatthecollisionprobabilityscaleswiththetimea
moleculespendsinthehighpressureregionor,equivalently,with1/v,wherevis
themolecule’svelocity.Insection3.3,thisassumptionwillbeusedasthebasisof
themodelforthebeamformation.

3.3Modelofvelocityfilteringincludingcollisionallosses

33

Comparingthemeasurementsat300Kand200KinFig.3.1(b)itshouldbe
notedthatnotonlytheshapeofthecurvesbutalsotheoptimalpressuresfora
givenelectrodevoltageareidentical.Measurementsofthepressureinthevacuum
chamberhousingthenozzle,whichhavebeenperformedataconstantreservoir
pressurebutfordifferenttemperaturesofthecoolingstage,indicatethatthetotal
lineconductanceisindependentofthetemperatureofitslastsection(thenozzle).
Hence,thegasflowthroughthenozzleforagivenreservoirpressuredoesnotdepend
onthetemperature.Theprobabilityforaslowmoleculetoundergoacollisionin
the“highpressureregion”isthesameforthe300Kand200Kmeasurement,since
thesamefluxofmoleculesisstreamingoutofthenozzle.Thereforeoneobserves
thesamedependenceonreservoirpressure,independentofthenozzletemperature.

3.3Modelofvelocityfilteringincludingcollisional
lossesTheeffectofcollisionsisincludedintothetheoryofvelocityfilteringpresentedin
section2.1asfollows.Theprobabilityforaslow,inprincipleguidablemoleculeto
undergoacollisionwithsomefastmoleculeisproportionaltothetimetcwhichthe
slowcollisionmoleculethevelospecitndsyofinatheslowregionmoleculewhereislikelycollisionstoareincrease.mostAsaprobable.consequenInsucce,hita
overcannotthebetransvguidederseanextenymore.tofSincethenoguidelargeinveachariatplaneionofattheagivgasendensitdistanceyisexpfromectedthe
hasnozzle,notheinfluencetransvonersethepositioncollisionandthereprobabilitbyythe.Hentransvce,ersethevelocitprobabilityofytheforamoleculesslow
moleculetobelostfromtheguidedbeamisinverselyproportionaltothemolecule’s
anlongitudinaladditionalvelofactorcityvexpz(due−tob/vtc)∝is1/vzincluded.Toinaccounthetforlongitudinalthisvelovcitelocity-depyendendistribution.tloss,
zThemodelforvelocity-dependentcollisionallossesresultsinamodifiedlongitudinal
velocitydistributionfb(vz)
fb(vz)dvz=N1exp(−b/vz)exp(−vz2/α2)dvz,(3.1)
towhere∞vNisf(av)dconstanv=t1.suchthatthetotalfluxcomingoutofthenozzleisnormalized
0Figurezb3.2zshowsztheeffusiveaswellasthemodifiedlongitudinalvelocitydistri-
butionsofammonia(ND)moleculesemergingfromthethermalsourcefordifferent
valuesoftheparameter3b.Becausethecollisionprobabilitydependslinearlyon
thefluxoutofthenozzle,theparameterbisexpectedtodependlinearlyonthe
morereservoirreducedpressure.forItlargercanvbalueseseenofb.thatFigurethe3.2fractionalsoofshoslowswthatmoleculestherisingismoreslopeandof
vtheelovcitieselocitywithb.distributionTherefore,oftheweshortlymoleculesspeakcomingofaboutoofostingtheofnozzlethebeamshiftsandtocalllargerb

34Collisionaleffectsintheformationofcoldguidedbeamsofpolarmolecules

ofFigureammonia3.2:(ND(a)3)Longitudinalmoleculesveloemergingcityfromdistributionsthethermalincludingsource.thebShoownostingaretermvzdistributionsfb(vz)
0.1formbardifferen(bt=40valuesm/s)ofandthe1.0bomostingbar(b=400parameterm/s)b,inthecorrespexpondingerimentot,inreservoircomparisonpressurestotheof
velocitydistributionofanidealeffusivesource.Guidablevelocitiesareindicatedfora
1−saStarklongitudinalshiftofΔWcutoff=2velocmcityatofan230m/sappliedforNDtrapping3.(b)iselectricazofieldominofto100thekV/cm,regionofresultingguidablein
cities.elov

theboostingparameter.Thiseffectisobservableinexperimentswithsmallelectrode
voltages.Atthesesettingsonlytheslowestmoleculeswhicharemostaffectedby
theboostingareacceptedbytheguide,whichstronglyaffectsthemeasuredsignals.
Boostingcanalsobeobservedforhigherelectrodevoltages,whenthereservoirpres-
sureisincreased.Thisresultsinlargerboostingeffects,whichinfluencealsofaster
molecules.Atveryhighreservoirpressures,theresultingbeamwillhaveanarrow
velocitydistributionlocatedatahighvelocity.Suchfree-expansionbeams[Pau00]
havehighintensity,butduetothelackofmoleculeswithlowvelocitytheyarenot
compatiblewiththeelectrostaticvelocity-filteringandguidingtechnique.Therefore,
theseexperimentsareperformedinthenear-effusiveregime.There,theboostingis
relativelysmallandareasonableamountofslowmoleculesispresentinthebeam
orifice.sourcethefromemergingThefluxofguidedmoleculesΦ(U)asafunctionoftheelectrodevoltageUcan
becalculatedbyintegrationoverthevelocitydistributionsuptothelongitudinal
andtransversecutoffvelocitiesasdescribedinsection2.1.Thefactorexp(−v2/α2)
isneglected,sincevα.Thisresultsin
vmaxvmaxvl,max
Φ(U)=f1D(vx)f1D(vy)vzfb(vz)dvxdvydvz
vx=−vmaxvy=−vmaxvz=0(3.2)
vl,maxvl,max
∝v2maxvzexp(−b/vz)dvz∝Uvzexp(−b/vz)dvz,
vz=0vz=0

3.4Electrode-voltagedependenceofvelocityfiltering35
√swhereIntheuseexphasebrimeneenmts,adehowofevver,max,vthel,maxQMS∝ΔWmeasuressandΔdensitWy,∝asU.discussedinsec-
tion2.4.Sincethedensitynisconnectedtothefluxbyn=Φ/v,thesignalof
guidedmoleculesS(U)isgivenby
vmax,lS(U)∝Uexp(−b/vz)dvz.(3.3)
=0vzinSWithout(U)∝anUy3b/2o.Fosting,ori.e.,non-zerovassumingaluesaofpbtheerfectlyelectreffusivodeevsouroltagece(bde=p0),endencethisofresultsthe
mensignalts[ofRan03guided,mJun04a,oleculesRie06is,moMot09bdified.],ThiswhereahasdepbeenendenceobservofedtheinformpreviousS(U)exp∝eri-U2
wwithasextractedquadraticforStarkmoleculesshifts.TwithhisissuelinearisStarkaddressedshiftsinandmoreS(U)detail∝atU4theforendofmoleculesthe
section.wingfollo

3.4Electrode-voltagedependenceofvelocityfil-
teringtheFigureapplied3.3showselectrothedevsignaloltageofforguideddifferentammoniasettings(NDof3)themoleculesreservoirasapressure.functionTheof
dataoftheindividualvoltagescansisnormalizedtothefitvalueat±6kVelec-
trodevoltage.ThesolidcurvesarefitsusingEq.(3.3)whichtakesintoaccountthe
depletionofslowmoleculesfromtheguidedbeamduetocollisions.Thefollowing
boostingparametersaredeterminedfromthesefitsfortherespectivereservoirpres-
sure:b=20m/s(0.01mbar),b=80m/s(0.1mbar),b=400m/s(1.0mbar).Several
featurescanbeobservedfromthisfigureandthefitresults.Increasingthereser-
voirpressureresultsinmorecollisionsandalargerboostingparameter.Therefore,
alargerfractionofslowmoleculesisdepleted,causingarelativelysmallersignal
atcauseslowertheelecurvctroedeinvtheoltageslin-linatplot,whichFig.only3.3the(a),slotowbestendmstrongerolecules.Fareromguided.thelog-logThis
plot,observFig.ed.3F.3or(b),electrothedevdifferenoltagestcharabovactere±of(1–2)thevkVoltagethefitdepcurvendenciesesfortcanhe0.01clearlymbarbe
theandslop0.1emofbarthefitmeasuremencurvectshangesarewithnearlyreservstraigoirhtlinespressure,intheindicatinglog-logplot.differenHotpwoevwer,er
laws.Thedeviationsforsmallelectrodevoltagesmaybeexplainedbythebehavior
oftheStarkshift:ForsmalltrappingelectricfieldstheStarkenergyoftheND3
moleculesbecomescomparabletotheinversionsplitting,whichleadstoquadratic
Starkshiftsandthereforeasmallerfractionofguidedmolecules.
ThedatashowninFig.3.3aretakenat300Ksourcetemperature.Forasource
temperatureof200Kexactlythesamebehaviorisobserved.Thesameeffect,i.e.,no
influenceofthesourcetemperature,wasalreadyfoundinthepressure-dependence

36

Collisionaleffectsintheformationofcoldguidedbeamsofpolarmolecules

Figure3.3:(a)Dependenceofthesignalofguidedammonia(ND3)moleculesonthe
moelectrodel,deEq.v(3.3oltage),forwhichdifferenaccounttsreservforoircollisionspressures.intheThecurvhigh-presearessureindividualregion.Thefitsfollousingwingthe
bbo=20ostinm/sgpar(0.01ammetersbar),areb=80m/sdetermined(0.1mfrombar),theseb=400fitsm/sforthe(1.0mrespbar)ectiv.e(b)resshoervwsoirthepressure:same
pdataerimenandtalfitdatacurvandesthewithmodellogarithmicoversevaxeseraltoordersillustrateofthemagnitudegoodinreservagreemenoirtbetpressureweenandex-
signal.

studydiscussedinsection3.2.Sincethefluxofmoleculesoutofthenozzledoesnot
changewithtemperatureinthepresentsetup,thecollisionprobabilityforaslow
moleculeshowsthesamedependenceonthereservoirpressure,independentofthe
erature.tempsourceAccordingtothedevelopedmodelforthecollisionallosses,theboostingparameter
bisexpectedtodependlinearlyonthefluxofmoleculesoutofthenozzle.Asalready
discussed,theboostingparameterbincreaseswithenlargedreservoirpressure(see
Fig.3.3).However,thisincreaseisnotlinear.Especiallyatlowelectrodevoltages
theobservedsignalofguidedmoleculesmightbereducedbyothereffectsthan
boosting,suchasquadraticStarkshiftsforsmallelectricfields.Thisreductionof
themoleculesignalcouldresultintoolargefitvaluesfortheboostingparameterb.
Tocircumventthisproblem,anotherapproachischosentotestthelinearde-
pendenceoftheboostingparameteronthereservoirpressure.Forhighreservoir
pressures,resultinginahighfluxofmoleculesoutofthenozzle,relativelyfastmo-
leculesareaffectedbytheboostingaswell.Theboostingisthereforevisibleat
higherelectrodevoltages,whereabettersignal-to-noiseratioofthesignalofguided
moleculesisachieved.Furthermore,theabsolutemoleculelossduetocollisionalef-
fectsislarger,increasingthedeviationsfromanidealeffusivesource.Therefore,the
measurementatthehighreservoirpressureof1.0mbarisusedasareference.Then,
theboostingparameterobtainedfromthefittothedatatakenat1.0mbarisscaled
linearlywithreservoirpressure.Fig.3.4showstheelectrode-voltagedependenceof
thesignalofguidedmoleculestogetherwithcurvesofthemodelEq.(3.3)using

3.4Electrode-voltagedependenceofvelocityfiltering

37

Figure3.4:Dependenceofthesignalofguidedammonia(ND3)moleculesonthe
electrodevoltagefordifferentreservoirpressures.ThesamedataareshownasinFig.3.3.
Totestthelineardependenceoftheboostingparameteronthereservoirpressure,thedata
at1.0mbarhasbeenfittedwiththemodel,Eq.(3.3),whichtakesintoaccountcollisions
inthehigh-pressureregion.Thisfitgivesaboostingparameterb=400m/s.Fortheother
curvestheboostingparameterdeterminedat1.0mbarisscaledlinearlywithpressure,
b=40m/s(0.1mbar)andb=4m/s(0.01mbar).

thesescaledvaluesoftheboostingparameterb.Thedataarewelldescribedbythe
curvesovertheinvestigatedrangeofreservoirpressures,whichspanstwoordersof
magnitude,therebyverifyingthemodelofpressure-dependentcollisionallosses.
ToconnectthemodelforthesignalofguidedmoleculesS(U),whichincludes
collisionsinthehigh-pressureregion,topreviousexperiments,thedataarefitted
withU3/2andU2polynomials.Figure3.5(a)showsthedependenceofthesignal
ofguidedmoleculesforverylowreservoirpressure(0.01mbar).Forvoltagesabove
±(1–2)kVthedataarewelldescribedbyaS(U)∝U3/2dependencerepresented
bythesolidline.Thisisexactlytheelectrode-voltagedependenceexpectedforan
idealeffusivesource,asdiscussedinsection3.3.
Figure3.5(b)showsthesignalofguidedmoleculesatamediumpressure(0.1mbar).
Formostexperimentsutilizingtheguide,thesourceisoperatedinthisrangeofpres-
sures[Jun04a,Mot09b].Here,thedataareshowntogetherwithafitofaS(U)∝U2
electrode-voltagedependence.Inearlierexperiments[Ran03,Jun04a,Rie06]the
goodagreementbetweentheexperimentaldataandtheS(U)∝U2modelsuggested
afluxmeasurementincombinationwithanidealeffusivesource.Forcalibrationsof
fluxesanddensitiesofguidedmolecules,however,aQMSsignalproportionaltothe
densityofmoleculesintheionizationvolumewascorrectlyassumed.Theimproved
setupusedfortheexperimentspresentedinthisthesisallowedsystematicmea-
surementsofthesignalofguidedmoleculesalsoforverysmallreservoirpressures.
ThesestudiesconfirmthatthesignaloftheQMSisproportionaltothedensityof
theguidedmoleculesintheionizationvolumealthoughitdependsquadraticallyon
theelectrodevoltage.

38

Collisionaleffectsintheformationofcoldguidedbeamsofpolarmolecules

Figure3.5:Dependenceofthesignalofguidedammonia(ND3)moleculesontheelec-
trodevoltagefordifferentreservoirpressures.The3/2samedataareshownasinFig.3.3and
(b)Fig.S(3.4U.)∝TheU2curvforesthearemediumfitsusingpressure(a)Sof(U0.1)∝mUbarforemplotheyedloinwmostpressureguidingof0.01expmbarerimenandts.

3.5Velocitydistributionsofguidedmolecules

Additionalinformationontheguidedbeamofpolarmoleculescanbeobtainedfrom
avelocitydistribution,whichisconstructedfromthetime-resolvedQMSsignal
asdiscussedinsection2.5.Thesevelocitydistributionsrepresentanother,even
moredirect,methodtolookattheboostingfeaturecausedbycollisions.Thiscan
beobservedbycomparingnormalizedvelocitydistributionsdeterminedforfixed
electrodevoltagebutfordifferentreservoirpressuresinFig.3.6.Forincreasing
reservoirpressures,thevelocitydistributionshiftstohighervelocities.Asexpected,
thecutoffvelocityonthehigh-velocitysidestaysthesame,becauseitdependsonly
onthedominantStarkshiftoftheguidedmoleculesandontheguidegeometry.
Moleculeswithavelocityexceedingthiscutoffvelocitycannotbeguided.Thisalso
explainstheshapeofthepressuredependencecurvediscussedinsection3.2:For
increasingreservoirpressure,largerandlargerpartsofthevelocitydistributionof
moleculesintroducedintotheguideareshiftedbeyondthecutoffvelocity.Thereby,
thefractionofmoleculeswithvelocitiesacceptedbytheguidedecreases.
Comparingthevelocitydistributionsfor±3kVand±5kVelectrodevoltagein
Fig.3.6(a)andFig.3.6(b),oneobservesashiftinthecutoffvelocityaswellasin
thepositionofthemaximumofthedistribution.Thereasonforthisistheincrease
ofthetrappingfieldwithelectrodevoltage.Atlargertrappingfieldsalargervelocity
rangeofmoleculesisacceptedbytheguideasalreadydiscussedinsection2.1.
Ifoneisinterestedonlyintheslowestmoleculesfromthevelocitydistribution,
increasingthepressureforanincreaseinguidedsignaliscounterproductive.Asdis-
cussedinsection3.2,thepressurefortheoptimalsignalofguidedmoleculesshifts
tosmallervalueswithreducedelectrodevoltage.Thiscanbeobservedfromthe
velocitydistributionaswell.Forexample,atareservoirpressureof1.0mbar,the

3.5Velocitydistributionsofguidedmolecules

39

Figure3.6:Normalizedvelocitydistributionsfordifferentammonia(ND3)pressuresin
thereservoir.Theeffectofcollisionsisvisibleasashiftofthevelocitydistributiontowards
highervelocitiesforincreasingreservoirpressure,whilethecutoffvelocitystaysthesame.
Comparingthevelocitydistributionat(a)±3kVand(b)±5kVelectrodevoltage,the
largerguidingelectricfieldleadstoanincreaseinthelongitudinalcutoffvelocityaswell
astoashifttowardshighervelocitiesofthemaximumofthedistribution.

slowestmoleculesobservedintheexperimenthavevelocitiesofaround35–40m/s,
whileatareservoirpressureof0.1mbarmoleculesdownto25m/sareobserved.
Especiallyinthe±3kVmeasurementitcanbeseenthatbydecreasingthepressure
from0.1mbarfurtherto0.01mbar,therisingslopeofthevelocitydistributionis
slightlyshiftedtolowervelocities.Thisisinagreementwiththevoltagedepen-
denciesshowninsection3.4,whichalsoshowanincreaseinthesignalofguided
moleculesforlowvoltages,correspondingtoslowmolecules,whenthepressureis
reducedthatway.Evenforthisverysmallreservoirpressure,extrapolationofthe
risingslopeofthevelocitydistributiondoesnotcutthevelocityaxisatzeroveloc-
ity.Measurementsoftheelectrode-voltagedependenceforlow(0.01mbar)reservoir
pressureshowaswellthatforsmallelectrodevoltageslessmoleculesaredetected
thanexpectedfromtheS(U)∝U3/2powerlawvalidforapurelyeffusivesource(see
Fig.3.5).Thisindicatesthatevenforsuchreducedpressurescollisionsstillplaya
rolefortheslowestmoleculescomingoutofthenozzle.Inthe±5kVmeasurement
thiseffectislessvisible.Thiscanbeattributedtotheverylimitedsensitivityof
thetime-of-flight(TOF)methodonthelowvelocityside.Forthelowestvelocity
inthedistribution,thetime-of-flightsignalhasalreadyreachednearly99%ofthe
steadystatevalue.Therefore,therisingslopeofthevelocitydistributionmightbe
moresusceptibletosystematicerrorsevenafterrejectingthelong-timedatabythe
ostselection.pFormanyapplicationstheboostingshouldnotbeaproblem.Whenthereservoir
pressureisincreased,themaximumofthevelocitydistributiondoesnotshifttoo
much:Foranincreaseofthereservoirpressurefrom0.1mbarto1.0mbartheshift
isonly≈25m/sat≈100m/speakvelocityat±5kV.Nonetheless,thisriseofthe

40Collisionaleffectsintheformationofcoldguidedbeamsofpolarmolecules

reservoirpressureincreasesthefluxofguidedmoleculesandtherebythedetector
for,signale.g.,byspafactorectroscopicoffiveasstudiesshownwhereinaFig.high3.1.densitThisyofmakcolesdthemoleculessourcevwithineryaattractivcertaine
velocityintervalisdesirable.

Summary3.6Inthischapter,theperformanceoftheelectricguideoverawideparameterrange
wasdescribed.Thisallowstoverifyamodelforthebeamformationtakinginto
accountcollisionsinandnearthenozzle.Incomparisontoanidealeffusivesource,
theseextractioncollisionsofslowreducemoleculesthefractiofromntheofsloreservwoir.moleculesByopanderatingtherebinyathededicatedefficiencypres-for
cansureberange,achievhoed.wever,Theaneffectsoptimizedofcollisionsfluxofinthmoleculeseformationuptoaofgivtheenbeammaximalarevelodirectcitlyy
observedinthevelocitydistributionsaswellasinthecharacteristicshapeofthe
electrode-voltagedependenceofthesignalofguidedmolecules.Theresultsarein
agreementwithexperimentsemployingacryogenicheliumbuffer-gascellforcool-
ingofthemolecules,wherethesourceperformanceislimitedonlybytheboosting
forincreasingheliumdensities[Som09,vB09].Alreadywiththeroom-temperature
source,thebeamsproducedbytheelectricvelocity-filteringandguidingtechnique
arewellsuitedforcollisionexperiments[Wil08a,Wil08b,Bel09a]orspectroscopic
[Rie06applications,,Mot07,sinceMot09bthey].comThebineadetailedhighcontinunderstandinguousfluxofwithethaelectricrelativguideelyashighapuritsourcye
fore.g.,coldforploadingolarofmoleculesanelectrostaticenablesmoretrapforinsightmoleculesforthe[Rie05design].ofThere,futurefurthexpercoerimenolints,g
ofthemoleculescanbeinvestigated.Proposedschemesincludecollisionwithsimul-
taneouslytrappedultracoldatoms[Rie07a,Rie07b,Sch07b,Sch08]orcombinations
ofsuitablytailoredtrappingelectricfieldsandinfraredtransitions[Zep09].Alsothe
developmentofanewsourcededicatedtoexperimentswithonlytheslowestmolecu-
lesbenefitsfromtheseresults.Theelectricguidingtechniqueoffersmanyprospects
forfutureexperimentsbyprovidingastartingpointfornewcoolingschemes.

Chapter4

Coldguidedbeamsofwater
ologsisotop

Inthischapter,electrostaticvelocityfilteringandguidingisstudiedforthedifferent
waterisotopologsH2O,D2O,andHDO.Althoughthesemoleculesseemverysimilar
atafirstglance,whenexposedtoexternalelectricfieldstheyshowasurprisingly
differentbehaviorduetotheirdistinctStark-shiftproperties.Thereasonforthis
isfoundintheirdifferentgeometrywithrespecttotheorientationoftheelectric
dipolemomentrelativetotheprincipalaxes,asillustratedinFig.4.1.

Figure4.1:Orientationoftherotationalaxesin(a)D2Oand(b)HDO.Thea-and
b-axeslieintheplanespannedbythemolecularbonds.InD2O(andH2O),theelectric
dipolemomentdisorientedsolelyalongtheb-axis.Keepingthepositionsofthenuclei
fixed,theprincipalaxes(a,b)inHDOarerotatedaroundthec-axisrelativetothe
situationinD2O(dashedaxes,a,b).Asaresult,acomponentofthedipolemoment
alongthea-axisispresentinHDO.

Inchapter2itwasshownhowtheefficiencyofelectrostaticvelocityfilteringand
guidingdependsontheratiobetweentheStarkshiftandthemassofthemolecules
ofinterest.Thisparameterdependenceofthevelocity-filteringprocesscanbestud-
iedinadistinguishedwaybyexperimentsemployingthedifferentwaterisotopologs.
Duetotheirsimilarchemicalproperties,nolargeinfluenceofuncontrollablesystem-
aticeffectsonthemeasurementoutcomeistobeexpected.Thesestudiesallowfor

41

42

Coldguidedbeamsofwaterisotopologs

importantconclusionsontheinfluenceofinternalmolecularstates,andespecially
theirStarkshift,ontheefficiencyofelectrostaticvelocityfilteringandguiding.Fur-
thermore,theyillustratetheversatilityoftheelectrostaticguideasacoldmolecule
sourceapplicabletodifferentspeciesofpolarmolecules.
Todescribethebehaviorofthedifferentwaterisotopologsinexternalelectric
fields,thetheoryfortheStarkshiftofasymmetric-rotormoleculesispresentedin
section4.1.TheresultsofnumericalcalculationsofmolecularStarkshiftsforthe
waterisotopologsarethendiscussed,andthecharacteristicdifferencesarerelated
tothespecificrotationalstructureofthemolecules.Insection4.2itisshown
howthecalculatedStarkshiftsofH2O,D2O,andHDO,thefilteringproperties
oftheguide,andthethermalpopulationsinthemoleculesourcecanbeusedto
makepredictionsoftheguidedflux.Themodificationsmadetotheexperimental
setuptoallowforsystematicguidingexperimentswiththewaterisotopologsis
brieflydescribedinsection4.3.There,mainlythequestionisaddressedhowthe
contributionsoftheindividualisotopologstotheguidedbeamcanbeobtainedfrom
theintegratedmassspectrometersignal.Afterthisdiscussion,theexperimental
resultsarecomparedtothetheoreticalpredictionsinsection4.4andsection4.5.
ThedifferencesinStarkshiftbetweentheisotopologsaredirectlyevidentfromthe
characteristicdependenceofthesignalofguidedmoleculesontheappliedelectrode
voltage.VelocitydistributionsallowforanalternativepointofviewontheseStark-
shiftproperties,andconfirmthegoodagreementbetweenthemeasurementsand
predictions.theoreticalthe

4.1Starkshiftofthewaterisotopologs

isAsshowdeterminednincbyhaptether2,Starkthefluxshiftofofguidethatdstate.moleculesTheintoatalfluxcertainisrotatithenonalgivenstateby
thesumoverthecontributionsofallthestateswhicharethermallypopulatedin
enthetwatermoleculeisotopsource.ologs,TotheirmakeStarkashiftstheoreticalmustpredbeictioncalculated.fortheInfluxessectionofthe4.1.1itdiffer-is
shownhowtheseStarkshiftsarecalculatedbynumericaldiagonalizationofthe
asymmetric-rotorHamiltonianinthepresenceofanexternalelectricfield,following
theproceduregivenbyHainetal.[Hai99].Foranintroductiontothetheoretical
descriptionofasymmetric-rotormolecules,thereaderisreferredtotextbookson
particularmolecular[phAll63ysics,inBun05,generalBun06[,Dem03bGor70,,Hak03Her45],andHer50on,Kro75micro,wTaovew75sp,Zar88ectroscop].ySec-in
tion4.1.2thenillustrateshowthesymmetrypropertiesandtheorientationofthe
electricdipolemomentofthedifferentwaterisotopologsaredisplayedinthespecific
shifts.Stark

4.1Starkshiftofthewaterisotopologs

43

H2OHDOD2O
RotationalA27.7923.4815.39
constantsB14.509.137.26
(cm−1)C9.966.404.85
Dipole-momentµA00.660
componentsµB1.941.731.87
(Db)µC000
Table4.1:Rotationalconstantsandcomponentsoftheelectricdipolemomentalongthe
principalaxesforthedifferentwaterisotopologsH2O,D2O,andHDO[Tow75,Bri72],
whichhavebeenusedforthecalculations.
DuringthecompositionofthisthesisandafterpublicationofM.Motschetal.,Phys.Rev.
A79,013405(2009),differingvaluesforthedipolemomentofH2Owerefoundinthe
literature:µB=1.94Db[Gol48,Tow75],µB=1.86Db[Bir52,Clo73,Dyk73,Lid90,Sho91].
ThesedatasuggestthatthevalueµB=1.94Db,whichwasextractedfromA.L.Townes
andC.H.Schawlow,MicrowaveSpectroscopy[Tow75],hasbeensupersededbythevalue
µB=1.86Db.SincetheStarkenergyisdeterminedbytheproductofthedipolemoment
andtheelectricfield,thisdifferenceof5%inthevalueofthedipolemomentonlyleads
toarescalingoftheelectricfieldatwhichagivenStarkshiftisreached.Duetothesmall
magnitude,nosignificantinfluenceontheresultspresentedinthischapterisexpected.

shiftsStarkofCalculation4.1.1WhenaclassicalelectricdipoledissubjecttoanexternalelectricfieldE,itsenergy
ΔWsdependsontherelativeorientationbetweenthetwovectors,ΔWs=−d∙E
[Jac99,Dem99].Forparallel(antiparallel)orientationthedipolewillminimizeits
energyforhigh(low)electricfields.Therefore,onereferstoadipoleinthetwo
situationsasahigh-fieldseeker(low-fieldseeker).
Consideringapolarmolecule,itsdipolemomenthasaspecificorientationrelative
tothebody-fixedcoordinatesystem.Themoleculeasawhole(andwithitthe
body-fixedcoordinatesystem)canrotatewithrespecttothespace-fixedcoordinate
system,inwhichtheexternalelectricfieldisapplied.Thismolecularrotationis
describedquantum-mechanically.Therefore,theorientationofthedipolemoment
inthespace-fixedframecanbeinferredfromthemolecularrotationalstate.The
Starkshiftofsuchamolecularrotationalstateisthencalculatedfromtheinteraction
betweenthemoleculardipolemomentandtheexternalelectricfield.Themolecular
propertiesrelevantforthesecalculationsarelistedinTbl.4.1.A,B,andCare
therotationalconstantsalongtheprincipalaxesofthemolecule,whereA(C)is
orientedalongtheaxiswithlargest(smallest)rotationalconstant,A≥B≥C.The
orientationoftherotationalaxesinD2OandHDOisillustratedinFig.4.1.
TheHamiltoniandescribingarigidrotatingmoleculeintheabsenceofexternal
electricfieldscanbewrittenas
Hrot=1(A+C)Jˆ2+1(A−C)H(κ),(4.1a)
22

44

Coldguidedbeamsofwaterisotopologs

tationRepresenIrIIrIIIr
acbxbacycbazTable4.2:Thethreepossibleconnectionsbetweentheprincipalaxesofthemolecule
(a,b,c)andtheright-handed,body-fixed,coordinatesystem(x,y,z).Xrdenotesthe
choiceofright-handedcoordinatesystems,whereXequalstherepresentationsI,II,or
III.(Tableadaptedfrom[Kin43].)
tationRepresenIrIIrIIIr
F21(κ−1)021(κ+1)
-1κ1GH−21(κ+1)121(κ−1)
Table4.3:CoefficientsusedinthematrixelementsofthereducedHamiltonian,Eq.(4.2),
forthedifferentrepresentationslistedinTbl.4.2.(Tableadaptedfrom[Kin43].)

HamiltoniandreducethewithH(κ)=Jˆa2+κJˆb2−Jˆc2.(4.1b)
Theconstantκ=(2B−A−C)/(A−C)isthesocalledasymmetryparameter,
takingthevalue−1inthelimitoftheprolatesymmetrictop(A=B)and+1in
thelimitoftheoblatesymmetrictop(B=C).Jˆisthetotal-angular-momentum
operator,andJˆi(i=a,b,c)aretheprojectionsofJˆonthefigureaxes,withJˆ2=
Jˆa2+Jˆb2+Jˆc2.Inthecalculations,thisHamiltonianisevaluatedinthesymmetric-rotor
basis.Thenon-zeromatrixelementsofthereducedHamiltonianH(κ),Eq.(4.1b),
inthesymmetric-topbasis{|JKM}aregivenby
JKM|H(κ)|JKM=FJ(J+1)−K2+GK2,(4.2a)
J,K±2,M|H(κ)|JKM=H[f(J,K±1)]1/2,(4.2b)
with1f(J,K±1)=4[J(J+1)−K(K±1)]×[J(J+1)−(K±1)(K±2)].(4.2c)
ThecoefficientsF,G,HaresuppliedinTbl.4.3.Onlysymmetric-rotorstateswith
ΔK=0,±2arecoupledbytheasymmetric-rotorHamiltonianascanbeseenfrom

4.1Starkshiftofthewaterisotopologs

45

KaKcEC2aC2bC2cD2
ee1111A
eo11-1-1Ba
oo1-11-1Bb
oe1-1-11Bc
Table4.4:Symmetryspeciesoftheasymmetricrotor.eandorefertotheparity(even
orodd)ofthequantumnumbersKaandKc,respectively.E,C2a,C2bandC2carethe
symmetryoperationsofthefourgroupD2,whereEistheidentityoperation,andC2i
performsarotationbyπaroundthei-axis.D2designatesthesymmetryspeciesofthe
].Bun06[groupfour

beEq.(found4.2).byThediagoneigenstatesalizationAofJτMtheandfullenergiesasymmetric-rotorWJτMoftheHamasymmeiltonian,tricEq.rotor(4.1acan),
yieldingWJτM=21(A+C)J(J+1)+21(A−C)WJτM(κ)(4.3)
and

AJτM=aJKτMΨJKM.(4.4)
KInthisexpression,theeigenstatesAJτMoftheasymmetricrotorareexpressedas
linearsuperpositionofsymmetric-rotorwavefunctionsΨJKM.Notethatthetotal-
angular-momentumquantumnumberJanditsprojectiononaspace-fixedaxisM
arestillgoodquantumnumbersinthefield-freeasymmetricrotor,incontrastto
K.Thiscanalreadybeseenfromtheasymmetric-rotorHamiltonianwhichdoes
notdependonMandwhichcommutateswithJˆ2.Thepseudoquantumnumber
τ=Ka−Kcisusedtolabeltheasymmetric-rotorstatesinascendingorderin
energy.τisdirectlyrelatedtothequantumnumbersKaandKcinthelimiting
caseoftheprolateandoblatesymmetrictop.Fromthesequantumnumbersthe
symmetrypropertiesoftheasymmetric-rotorstatescanbederived.InTbl.4.4the
symmetrypropertieswithrespecttothesymmetryoperationsofthefourgroupD2
[Bun06](sometimesalsoreferredtoasV(a,b,c)[Kin43])areshown.
AnexternalelectricfieldliftsthedegeneracybetweentheMsublevelsofastate
|J,τ.DifferentJstatesarealsocouplednow,leavingMastheonlygoodquan-
tumnumber.Ingeneral,anasymmetric-topmoleculecanpossesscomponents
ofitsdipolemomentµalongallthreeprincipalaxesinthebody-fixedframe,
µ=gµgeˆg,(g=a,b,c).AscanbeseenfromTbl.4.1andFig.4.1,thedipole
momentisorientedalongtheb-axisinH2OandD2O,whereascomponentsalongthe
a-andb-axisarepresentinHDO.ThisisimportantfortheirStark-shiftproperties,
sincedifferentcomponentspromotecouplingsbetweenrotationalenergylevelsof
differentsymmetryspecies.Thisaspectisdiscussedinmoredetailinsection4.1.2.

46

Coldguidedbeamsofwaterisotopologs

(FThe=X,electricY,Z),fieldEis=EZdefinedeˆZ.toThen,bethedirectedinteractionalongtheZHamiltonian-axisinisthegivspaceenby-fixedframe

(4.5)

Hs=EZΦZgµg,(4.5)
gSincewherethethedirectiondirectioncosinescosinesΦareFgtaconnectbulatedtheforspace-fixedsymmetric-rotortothewavemolecule-fixedfunctionsframonlye.
(seeTbl.4.5;notetherearesomemisprintsintheΦFgtabulatedin[Hai99]whichare
correctedhere.),theirmatrixelementswithrespecttotheasymmetric-rotorstates
harotorvewtoavbeefunctionsconstructed.intermThissofcanbedonesymmetric-rotorusingthestates,Eq.expansion(4.4of),theandresultsasymmetric-in

JτM|ΦZg|JτM=
J|ΦZg|JJM|ΦZg|JMδMM×aJKτMaJKτMJK|ΦZg|JK.(4.6)
KKNotethattheHamiltonianHsdescribingtheStarkinteractionwiththeexternal
electricfield,Eq.(4.5),onlycouplesstateswithΔM=0,duetothechoiceof
EalongtheZ-direction,E=EZeˆZ.BydiagonalizationofthetotalHamiltonian
Hrot+Hs(EZ)theeigenstatesandeigenenergiesoftheasymmetricrotorinthe
presenceofanexternalfieldcanbecalculated.TheStarkshiftΔWs(EZ)isthen
givenbythedifferencebetweenthetotalenergyintheexternalelectricfieldand
.nergyezero-fieldthe

4.1Starkshiftofthewaterisotopologs

22//112)]1)]1−222/1−/1−
/12]K2]M
11)KM
−−−J−J
222JJ()J()
(4[2K[2M
J4−−
JJ[([(JJ1)]+K±M±
[([(for].)Cro44[fromadaptedable(Trotor.symmetricthe
22//111−1)]++1)]
MKJ2J2J
(JJ()()
KM[4JJM1−222/1/1K
/J1|/12)]+/12)]+gF
223)]+22]Φ|
MKJMK±±−−1(21)+M,K,J
JJ22+J1)+(1)+1)+(1)+
J[(2JJKM([(1)±±22+JJ[([(J(4gFzFJ|xFgZJ|gXtselemenmatrixcosineDirection
11±±11±±KK,MM,
J|J|K,J|J|M,J|
Φ|Φ|yFΦ|Φ|gYΦ|
4.5:JΦ|Φ|
KJKJMJMJ
KJiMJi
able±T==

47

48

Coldguidedbeamsofwaterisotopologs

shiftsStarkofDiscussion4.1.2Theenergiesofthelowest-energeticrotationalstatesofthedifferentwateriso-
topologsinanexternalelectricfield,calculatedbytheproceduredescribedinsec-
tion4.1.1,areshowninFig.4.2andFig.4.3.Severalfeaturesaredirectlyevi-
dentwhencomparingthedifferentisotopologs.Firstofall,thecalculationspredict
quadraticStarkshiftsforH2OandD2O,whileforHDOlinearStarkshiftsarefound
aswell.Thisiscausedbythedifferentorientationsoftheelectricdipolemomentsin
themoleculeswithrespecttothemainaxesofthemolecule.InH2OandD2Othe
dipolemomentisorientedalongtheb-axis.InHDOthereisadditionallyacompo-
nentalongthea-axis.Thisisimportant,sinceinamoreprolateasymmetricrotor,
asisthecaseforthedifferentwaterisotopologs(H2Oκ=−0.49,D2Oκ=−0.54,
HDOκ=−0.68),thestateswiththesameKaquantumnumberwithinamanifold
ofstates{|J,Ka,Kc}withfixedJareneardegenerateforincreasingJandKa
quantumnumbers.Itisexactlythesestateswhicharecoupledbyadipolemoment
alongthea-axisinanexternalelectricfield.Hence,oncethecouplingbetweenthese
statesduetotheelectricfieldbecomeslargerthantheirasymmetric-rotorsplitting,
theStarkshiftbecomeslinear.ThisbehaviorisillustratedinFig.4.3forthelowest
energyrotationalstatesofHDOexhibitingamainlylinearStarkshift.ForH2Oand
D2Othesituationiscompletelydifferent,heretheStarkshiftsstayquadraticand
evenbecomesmallerwithincreasingrotationalenergyascanbeseenfromFig.4.4.
Asecondobservation,whichcanbemadefromFig.4.2,Fig.4.3,andFig.4.4,is
thatthemagnitudeoftheStarkshiftsoftheisotopologsalsodiffer.HDOexhibitsthe
largestStarkshifts,asistobeexpectedbecauseoftheirlinearcharacter.Besides,
theStarkshiftsofH2OaresignificantlysmallerthanthoseofD2O,althoughboth
moleculeshavesimilarsizedipolemomentsandhencesimilarcouplingsbetween
rotationalstates.Thereasonforthisisalsofoundintherotationalconstants.
SinceD2OhassmallerrotationalconstantsthanH2O,theenergylevelsarecloser
together,leadingtolargerStarkshiftsforcomparablecouplings,ascanbeseenfrom
.theoryerturbationpThethirdobservablefeatureisthattheStarkshiftsshowadifferentbehavior
withincreasingrotationalenergyforthedifferentisotopologs.InHDO,thestates
|J,τ,M=|J,J,JexhibitthelargestStarkshifts.AsindicatedinFig.4.4,theStark
shiftapproachesaconstantvalueforthesestates.Thisvalueisreachedforfull
alignmentofthedipole-moment’scomponentµaalongthea-axiswiththeelectric-
fieldaxis.TheStarkshiftsinH2OandD2Odecreasewithincreasingrotational
energy,aswasalreadyobservedanddescribedforD2ObyT.Riegeretal.[Rie06].
Forthesemoleculesthespacingbetweentherotationalenergylevelsincreaseswith
increasingJandKquantumnumbers,whichreducestheStarkshifts.

4.1

Stark

shift

of

the

aterw

ologsisotop

49

HDOFigureinan4.2:exLoterwenalst-energeticelectricfield.rotationalThesamestatesvoferticalthewscaleaterisisotopusedologsHthroughout2O,D2theO,fig-and
100ure.kV/cmStates(seewithTbl.con4.8)tributionsarep>lotted5%ininredtheandguidedmarkbedeambyaatastar.trappingelectricfieldof

50

Coldguidedbeamsofwaterisotopologs

shifts.FigureThe4.3:sameLowverticalest-energeticscaleisusedrotationalthroughoutstatesoftheHDOfigure.exhibitStatesingwithmainlyconlineartributionsStark
>plotted5%inwiththethickguidedredblineseamatandamarktrappingedbyelecatrstar.icfieldInofthis100figurekV/cmquan(seetumnTbl.umb4.8ers)Karea
theandKcareasymmetric-rotorusedtoindicatesplittingthebetcloseweenstatesconnectionwithtotheequalprolatequantumnsymmetricumbersrotor.JandThere,Ka
disappearssuchthattheyaredegeneratewithoutexternalelectricfields,givingriseto
ifts.hsStarklinear

4.1Starkshiftofthewaterisotopologs

51

Figure4.4:StarkshiftsofthedifferentwaterisotopologsH2O,D2O,andHDOatanelec-
tricfieldof130kV/cm.ThesolidcurveindicatestheBoltzmannfactorexp(−EJτM/kBT)
forscales.asourceThetempdifferenteratureMofstates293ofK.aOnlyrotationallfsstatesstate|areJ,τ,shoMwn.allhaNotevethethesamedifferentvrotationalertical
energybutdifferentStarkshifts,thusformingaverticalsequence.Notethatinthecase
ofHDOtheStarkshiftsapproachasaturationvalueforincreasingrotationalenergy.
Thisvalue,indicatedbythedashedline,correspondstothefullalignmentofthedipole-
rotorsmomenHt’s2OcompandDonen2OtthealongStarktheashifts-axisondecreasethewithelectric-fieldincreasingaxis.Inrotationalthecaseenergyof.theb-type

52

Coldguidedbeamsofwaterisotopologs

Figure4.5:Couplingsbetweentherotationalenergylevelsoftheasymmetricrotor,in-
ducedbythedifferentcomponentsofanelectricdipolemoment.Shownaretheenergy
levelsoftheasymmetricrotorfordifferentJquantumnumbersasafunctionoftheasym-
metryparameterκ.Thesymmetryoftherotationalstates,representedbythesymmetry
speciesofthefourgroupD2,isindicatedbythedashingofthecurves.Adipolemoment
µaalongthea-axismainlycouplesstateswhicharedegenerateintheprolatesymmetric
top,i.e.,κ=−1,whileadipolemomentµcalongthec-axismainlycouplesstatesdegen-
erateintheoblatesymmetrictop,i.e.,κ=+1.Thisneardegeneracygivesrisetolinear
Starkshiftsforthesestates.Incontrast,stateswhicharecoupledbyadipolemoment
µbalongtheb-axisarealwaysseparatedbyanintermediateenergylevel,therefore−1never
givingrisetoalinearStarkshift.Forthisfigure,rotationalconstantsA=10cmand
C=1cm−1wereused,withB=1...10cm−1varyinglinearlywithκ.

4.1Starkshiftofthewaterisotopologs

53

Moregenerally,theStark-shiftpropertiesdiscussedabovecanbeunderstood
foranarbitraryasymmetric-topmoleculebyexaminingitsrotationalenergy-level
structure,thesymmetrypropertiesofitsenergylevels,andthecouplingsbrought
aboutbythedifferentcomponentsofthemolecularelectricdipolemoment.These
couplingsbetweenrotationalstatesofthedifferentsymmetryspeciesarelisted
inTbl.4.6foranexternalelectricfieldalongtheZ-axis.Figure4.5showsthe
energy-levelstructureofanasymmetric-topmoleculeasafunctionoftheasymme-
tryparameterκforfixedvaluesoftotal-angular-momentumquantumnumberJ.
Thesymmetryoftherotationalenergylevels,representedbythesymmetryspecies
A,Ba,Bb,BcofthefourgroupD2,isindicated.Thecouplingsinducedbythedif-
ferentdipole-momentcomponentsµgaccordingtoTbl.4.6arealsoshowninthe
figure.AscanbeseenfromFig.4.5,foranear-prolateasymmetrictop,κ≈−1,the
energylevelswithsameKaareneardegenerate.Thesestatesarecoupledbya
dipolemomentµaalongthea-axis.ThisgivesrisetolinearStarkshifts,oncethe
Starkinteractionovercomesthesplittingoftheseenergylevelsintheasymmetric
rotor.Eveninthemostasymmetriccase,κ=0,thesplittingbetweenthestates
withhighestrotationalenergy,Ka=J,Kc=0,1,decreaseswithincreasingangular
momentum,ascanbeseenbycomparingtheenergy-levelcurvesforincreasingvalues
oftheJquantumnumber.ThisdiminishingsplittinggivesrisetolinearStarkshifts
inthelimitoflargeJforadipolemomentµaalongthea-axis,eveninthismost
case.asymmetricSimilarargumentsholdforanear-oblateasymmetrictop,κ≈+1.Here,the
energylevelswithsameKcareneardegenerate.Theseenergylevelsarecoupledby
adipolemomentµcalongthec-axis,leadingtolinearStarkshiftsasdiscussedfor
thenear-prolatecase.Onceagain,inthemostasymmetriccase,κ=0,linearStark
shiftsoccurinthelimitoflargeJ,howeverfordifferentrotationalstates.Thestates
Ka=0,1,Kc=J,beingcoupledbyadipolemomentµcalongthec-axis,showa
decreasingsplittingwithincreasingJ,whichgivesrisetolinearStarkshifts.
Thesituationis,however,completelydifferentforadipolemomentµboriented
alongtheb-axis.AscanbeseenfromFig.4.5,theenergylevelswhicharecoupled
bysuchadipolemomentarealwaysseparatedbyanotherenergylevelinbetween.
Therefore,thesplittingbetweenstatescoupledbyadipolemomentalongtheb-axis
neverapproacheszerowithinoneJsystem,independentofthevalueoftheasym-
metryparameterκ.Moreseverely,thesplittingbetweentheseenergylevelscoupled
byadipolemomentµbalongtheb-axisevenincreaseswithincreasingJ.Ascanbe
seenfromperturbationtheory,thisreducestheStarkshiftforincreasingrotational
energy(largeJ).Ofcourse,onecouldconsiderelectricfieldslargeenoughtocause
theStarkinteractiontoovercomethissplittingofrotationalstates.Nonetheless,
thisgenerallydoesnotleadtolinearStarkshiftsforlow-field-seekingstates.Cou-
plingtootherJstatesbecomesrelevantfirst,forcingallstatestobecomehigh-field
seeking.

54

Coldguidedbeamsofwaterisotopologs

Dipole-momentcomponentCoupledsymmetryspecies
µaA↔BaBb↔Bc
µbA↔BbBa↔Bc
µcA↔BcBa↔Bb
Tablemolecule4.6:byanCouplingsexternalbetelectricweenfieldtheapplieddifferentalongsymmetrythespspace-fixedeciesofZan-axis.Theasymmetric-rotormolecular
dipcouplingolemtoomenthetmaexternalyhavefield.compForaonentscouplingµginbettheweenbotwody-fixedframe,asymmetric-rotorwhichpstatesromote|iandthe
|fthetodipooleccur,momenthetµmatrixaisorienelementetdµgEalongZf|theΦZag|i-axis,mustthenotrelevvananish.tcompTogivonenetanΦZabexample,elongsif
tothesymmetryspeciesBa.Assuminganinitialstate|iwithsymmetryBc,applying
ΦconZa|itainsEresults.inTherefore,Ba◦Bc|f=Bmb.ustf|haΦveZg|iissymmetrynonzeroBbtoonlyfulfillifitsthisnon-reduciblecondition,sincerepresenBb◦Bbtation=
E.Asaresult,astatewithsymmetryBciscoupledtoastatewithsymmetryBbfora
dipolemomentalongthea-axis.

TheStark-shiftpropertiesexaminedintheprecedingparagraphscanbeunder-
stoodfromapurelyclassicalpointofviewaswell.Foraclassicalrotatingbody,
therotationisstablearoundtheaxisofsmallestandlargestmomentofinertia,
i.e.,thea-andc-axis.Aroundtheaxisofintermediatemomentofinertianostable
existsrotationaispnon-zeroossible.expIfectattheiondipvolealueofmomenthetisproorienjectiontedofalongthediptheolea-orcmomen-axis,tonththeree
directionofthespace-fixedelectricfield,exceptforaclassicalmotionwiththeaxis
ofrotationperpendiculartotheexternal-fieldaxis.Theprojectionofthedipole
momentdirectlyinteractswiththeappliedelectricfield,givingrisetoalinearStark
shift.Thissituationisfoundinthethecaseofasymmetrictoporforana-type
asymmetricrotorsuchasformaldehyde(H2CO).
Conversely,ifthedipolemomentisorientedalongtheb-axis,i.e.,theaxisof
inmomentermediatetonthemomenelectrictoffieldinertia,axistheisexpzero.ectationHence,valuetheofethexternalprojectionelectricofthefielddipfirstole
hastohindertherotationandorientthedipole,whichbecomesmoreandmore
difficultwithincreasingrotationalenergyandangularmomentum.Therefore,the
magnitudeoftheorienteddipoledecreaseswithincreasingrotationalenergy,in
accordancewiththedescriptiongivenbyquantummechanics.Thisorienteddipole
momentcantheninteractwiththeelectricfield.Thissecond-orderinteraction
givesrisetoaquadraticStarkshiftforb-typerotors.Thesameargumentholdsfor
linearheteronuclearmoleculeswithapermanentelectricdipolemoment,wherethe
rotationaveragesouttheprojectionofthedipolemoment.Hence,linearmolecules
exhibitaquadraticStarkeffectunlessanelectronicangularmomentumparallelto
theelectricdipolemomentµispresent,suchas,e.g.,inΠstatesofNH,OHorCO∗.
However,notethatinthecaseofaccidentaldegeneraciesalsoab-typeasym-
metricrotormayshowlinearStarkshiftsforcertainstates.Foranexamplesee,

4.2Calculationofthefluxofguidedmolecules

55

KaKcH2OD2OHDO
ee,oo161
eo,oe331
Table4.7:NuclearspindegeneracyfactorsgIforthethreewaterisotopologsH2O,D2O,
andHDO[Tow75].eandorefertotheparity(evenorodd)ofthequantumnumbersKa
andKcrespectively.

e.g.,theStark-energycurvesoftheb-typeasymmetricrotorCF2H2inFig.2in
Hainetal.[Hai99].There,thestate|J=2,τ=2,M=0isneardegeneratewith
|J=1,τ=0,M=0,towhichitiscoupledbyitsdipolemomentalongtheb-axis..
Themechanicalanalogueoftheseaccidentaldegeneracies,ifexisting,isnotevident.
Overallonecansummarizethatevenmoleculessuchasthethreewaterisotopologs
H2O,D2O,andHDO,seemingverysimilaratafirstglance,canshowsurprisingly
differentbehaviorwhenexposedtoanexternalelectricfield.

4.2Calculationofthefluxofguidedmolecules
AfterhavingobtainedtheStarkshiftsofthedifferentwaterisotopologs,thefluxes
ofguidedwatermoleculescanbecalculated.Thetotalfluxofguidedmoleculesfor
aspecificspeciesisobtainedbysummingoverthecontributionsofalltheindividual
internalstatestotheflux,weightedwiththeirthermaloccupationinthesource.
Thethermaloccupationofarotationalstate|J,τ,Minthesourceisgivenby
pJτM=1gMgIexp(−EJτM/kBT),(4.7)
ZwiththepartitionfunctionZ=JτMgMgIexp(−EJτM/kBT).Here,EJτMisthe
rotationalenergy,Tthesourcetemperature,gMtheMdegeneracyfactorofthe
state,andgIthenuclearspindegeneracyfactor.Nuclearspindegeneracyfactors
forThethefluxdifferenfortawgivaterenisotopguidingologselectricarelistedfieldincanbTbl.e4.7.expressedas
Φ=N0pJτMf(ΔWJsτM),(4.8)
MτJwiththeguidablefractionofarotationalstate|JτMgivenbyf(ΔWJsτM)∝
(ΔWJsτM)2asshowninsection2.1,andN0thenumberofmoleculesinjectedinto
theguidepersecond.FormoleculeswithonlylinearStarkshifts,ΔWJsτM(E)∝E,
thetotalfluxofguidedmoleculesisexpectedtoshowaquadraticdependenceonthe
trappingelectricfield,Φ∝E2,whenaneffusivesourceisassumed(seechapter3).
Similarly,formoleculeswithquadraticStarkshifts,ΔWJsτM(E)∝E24,aquartic
dependenceofthefluxonthetrappingelectricfieldisexpected,Φ∝E.
Figure4.6comparesStarkshiftsandcalculatedsourcepopulationsofindividual
rotationalstatesforH2OandD2O.Fromthisfigureitcanalreadybeanticipated

56

Coldguidedbeamsofwaterisotopologs

Figure4.6:CalculatedthermalspopulationsinthesourcepJτMatasourcetemperature
ofstates293|JK,,τ,andMofStarkH2OshiftsandΔD2WO.JτMStatesatanwithelectricthelargestfieldofcon130tributionskV/cmtoforthetheguidedrotationalflux
arelabeledwithquantumnumbers.

thatinthecaseofH2Othestate|J=1,τ=1,M=1willcontributestronglyto
theguidedflux.Thereasonforthelargethermalpopulationofthisstateinthe
reservoir,ascomparedtothe|J=1,τ=1,M=1stateinD2O,canbefoundin
thedifferentnuclearspinstatisticsofthetwoisotopologs.Forsuchconsiderations
basedonsymmetrypropertiesitisadvantageoustotransformfrom|J,τ,Mtothe
quantumnumbers|J,Ka,Kc,M.Forthestate|J=1,τ=1,M=1thisresults
inthecorrespondingquantumnumbers|J=1,Ka=1,Kc=0,M=1.According
toTbl.4.7,thisstateisfavoredduetothenuclearspinstatisticsinH2Oby3:1,
whileitisunfavoredinD2Oby3:6.
Theexpectedguidedfluxesofthedifferentisotopologscalculatedthiswayare
depictedinFig.4.7asafunctionoftheguidingelectricfield.Theguidedfluxes
ofthedifferentisotopologsdifferremarkablyinmagnitude.Furthermore,notonly
itsamountbutalsotheelectric-fielddependenceofthefluxofguidedmoleculesis
clearlydifferent.WhileH2OandD2Oshowaquarticdependenceoftheguided
flux,causedbyquadraticStarkshifts,theelectric-fielddependenceofHDOshows
amainlyquadraticbehavior,indicatingthepresenceoflinearStarkshifts.
Thecalculationsallownotonlypredictionsofthemagnitudeandelectrode-voltage
dependenceofthefluxesofguidedmolecules.Furthermore,itispossibletodeduce
thepopulationsofindividualrotationalstatesintheguidedbeam.Forthewateriso-
topologs,populationsofindividualrotationalstateswithcontributionslargerthan
5%ofthetotalfluxoftheconsideredisotopologsarelistedinTbl.4.8.Remark-
ably,thesinglestate|J=1,τ=1,M=1ofH2Ocontributes≈80%totheguided
fluxusingaroomtemperaturesource.Similarly,inD2Othemostpopulatedstate

4.3Experimentalprocedure

57

theFiguretrapping4.7:(a)electricCalculatedfield.Theguidedresultsfluxesoftheofthecalculationdifferentwdescribateredisotopinologssectionasa4.2arefunctionshownof
bythesymbols,whereasthesolidcurvesarequarticandquadraticfitstothecalculated
Theflux.guidedGuidedfluxfluxesofareHDOshonormalizedwsatothequadraticfluxdepofH2Oendenceataonthetrappingtrappingfieldof100electrickV/cm.field,
whereasforH2OandD2Oaquarticdependenceisfound.(b)isazoom-intocomparethe
calculationsoftheguidedfluxforH2OandD2Otoaquarticcurve.

|J=1,τ=1,M=1contributes≈21%tothetotalflux.Thereasonfortheselarge
populationsascomparedtoamoleculesuchasformaldehyde(H2CO)[Mot07]with
similarquadraticsizeStarkrotationalshiftbehaconstanvior.tsAsbutcanbmainlyeseenlinearfromStarkFig.4.4shifts,thecanbsizeeoffoundtheinStarkthe
leashiftvingonlydecreasesfewwithlow-energeticrotationalstatesenergywforithalargestmoleculeStarkwithshiftsaforquadraticguidingStark[Rie06shift,].
vIncerifiedhapterby5itcollinearisshouwnltrahovioletwsucsphectroscopcalculatedyinastatecoldpguidopulationsedbeamareofexpformaldeherimentallyyde
].Mot07[

4.3Experimentalprocedure
Toverifythetheoreticallyobtainedrelativefluxesofthedifferentwaterisotopologs,
expsetupaserimenthetsonewithHdescrib2O,edD2inO,sectandion2.2HDOwaswereused.pInerformed.thissection,Thesamethekeyexpfeatureerimenstalof
ofthethesetupindividualandsomeisotopexpologserimenaretalprohighlighcedurested.forWaterdeterminationmoleculesinofththeecgasonphasetributionsare
injectedintothequadrupoleguidethroughaceramictubewithdiameter1.5mm
andalengthof9.5mm.Thepressureinthereservoiriskeptatafixedintermediate
valueof0.10mbarviaathermoelectricallycontrolledflowvalve,resultinginagas
flowof1×10−4mbar∙l/s.Sincewaterhasasufficientlyhighvaporpressureof
≈25mbaratroomtemperature[Lid90],noheatingofitscontainerisnecessary.
Theconstituentsofthegasinjectedthroughthetubearemonitoredbyaresidual-

58

58Coldguidedbeamsofwaterisotopologs
sJτM(cmErot−1)p(%)SΔ(cmW−1)p(%)G
2101219542..7302..8900..0813797..43
313213.61.30.055.1
OH(a)2sJτM(cmErot−1)p(%)S(cmΔW−1)p(%)G
11122.70.540.2021.3
3-2174.50.830.1621.2
20249.30.940.1317.1
3-2074.50.420.1813.2
3-2274.50.830.108.0
OD(b)2sJτM(cmErot−1)p(%)S(cmΔW−1)p(%)G
333234.90.450.8315.0
424242407109..0800..198300..8959147..53
343224234297..9800..453300..585556..56
HDO(c)Table4.8:Propertiesofselectedrotationalstates(populationintheguide>5%)ofthe
threeSourcewpateropulationisotopforologsaHte2mpO,D2eratureO,ofand293HDO.K.ΔEWrots::StarkZero-fieldshiftatrotationalanelectricenergy.fieldpSof:
100kV/cm.pG:Populationintheelectricguideatanappliedelectricfieldof100kV/cm.

gasanalyzerplacedinthesourcevacuumchamber.Thisallowsadeterminationof
thecontributionsofthedifferentisotopologsduringeachmeasurement,asisfurther
explainedinappendixA.
Asshowninsection2.1,transverselyslowmoleculesinalfsstatearetrapped
bytheenclosinghighelectricfields.Alongitudinalcutoffvelocityisobtainedby
thebendsintheguide.Slowmoleculesareguidedaroundtwobendsandthrough
twodifferentialpumpingstagestoanultrahigh-vacuumchamber,wheretheyare
detectedbyaquadrupolemassspectrometer(QMS).Themoleculesareionizedby
electronimpactinacross-beamionsourceandmassselectedintheanalyzer.In
thefinalstageoftheQMSsingle-ioncountingisperformed.
ForguidingexperimentswithH2OandD2O,respectively,pureH2OorD2Oare
used.FormeasurementsemployingHDO,mixturesofliquidH2OandD2Owitha
ratioof1:1and4:1arepreparedinthecontainer.TheseresultinaHDOfraction

4.3Experimentalprocedure

59

Figure4.8:(a)Time-of-flighttracemeasuredwithHDOatanelectrodevoltageof±5kV.
ZoHighomvintooltagethe(HV)risingisslopswitceofhedtheonsignal,foranfromintervwhicalhofav250eloms,citywithadistribution50%dutcanybecycle.derived.(b)
Thesesignal-to-noiseplotsshowratiorawdata,illustratesi.e.,nothebacwidekgroundapplicabilitsubtractionyofhaselectrostaticbeenveloapplied.cityThefilteringexcellenandt
shiftsguidingsuctohas,differenforttypinstance,esofND3molecules.orH2CO,NotethethatQMSforsignalmoleculesofwithguidedmainlymoleculeslinearisevStarken
largerbyoneorderofmagnitude.

of≈48%and≈27%,respectively,comingfromthesourceasmeasuredwiththe
residual-gasanalyzer.Whenusingthesemixturesinthesource,allthreeisotopologs
areguidedsimultaneously.However,duetoitsmuchlargerStarkshiftforsome
rotationalstates(seesection4.1,andFig.4.4),HDOispreferentiallyguided.
Toextracttherelativemoleculesignalsofthedifferentisotopologsfromthese
measurements,somecorrectionsarenecessary,whichareexplainedinmoredetailin
appendixA.Firstofall,themeasuredioncountrateoftheindividualisotopologs
iscorrectedfortheirrelativecontributiontothegasinjectedintotheguideas
monitoredbytheresidual-gasanalyzerinthesourcechamber.Secondly,thefrag-
mentationoftheguidedmoleculesduringtheelectron-impactionizationintheQMS
hastobetakenintoaccount.
Theexperimentsareperformedasaseriesoftime-of-flightmeasurements.Here,
thehighvoltage(HV)isswitchedonandoffrepeatedlyinafixedtimingsequence.
Tosubtractbackgroundcontributions,thesignalofguidedmoleculesforthedifferent
isotopologsisdeterminedfromthedifferenceinthesteady-stateQMSsignalwith
HVappliedtotheguideandHVswitchedoff,asexplainedindetailinsection2.3.
Atypicaltime-of-flighttraceobtainedwithHDOisshowninFig.4.8.Althoughfor
moleculeswithmainlylinearStarkshiftssuchas,forinstance,ND3orH2CO,the
QMSsignalofguidedmoleculesislargerbyoneorderofmagnitude,anexcellent
signal-to-noiseratioisachieved.

60

Coldguidedbeamsofwaterisotopologs

electroFiguredev4.9:oltage.SignalShoofwnasguidedsolidH2O,curvDes2O,areandtheHDOtheoreticallymoleculesaspredictedafunctionsignalofdepappliedenden-
star.cies,NoteadjustedthattofitonlyD2oneOdataglobalat±6scalingkVfactorelectroisdevusedoltage.forallThistheordataypcurvointes.ismThearkeddifferenbyat
sloppropeserties.oftheH2curvOesandinDthe2OsdoublehowlaquarticogarithmicdepplotendencedirectlyoftheindicatesignaltheofdifferenguidedtStark-shiftmolecules
onquadratictheapplieddependenceelectricfield,indicatingindicatinglinearStarkquadraticshiftsStarkisfoundshifts,.whereasforHDOamainly

4.4Electrode-voltagedependence

wFigureater4.9isotopologscomparestothetheoutcomemeasuredoftheelectrode-vcalculationsoltagedepdiscussedendenciesinforsectionthe4.2.differenThet
calculationsarescaledbyonlyoneglobalscalingfactortoaccountfordetection
efficienciesandtheamountofgasinjectedthroughthenozzleintotheguide.Note
hasthatbnoeenremploelativeyed.scalingInthisfactorfigure,betthweeendetecthetorsignalcalculationsoftheforH2guidedO,Dw2aterO,andmolecuHDOles
iscomparedtothecalculatedfluxofguidedmolecules,albeittheQMSsignalis
propobservedortionalintosectionthe2.4densit.Hoywofever,guidedduetomoleculestheboarrivingostingofatthethebeam,ionizationthevelectroolumede-as
vinoltagesectiondep3.4,endenceinthecinhangesastermediatecomparedpressuretoanregime,idealwhiceffusivhewassource.usedAsfortheexplainedmea-
surementswiththewaterisotopologs,asimilardependenceofthedetectorsignal
ontheelectrodevoltageisexpectedasforafluxmeasurementemployinganideal
witheffusivelinearsource.(quaIndratic)particular,StarkSshifts.(U)∝DueU2to(Sthe(U)∝smallerU4)issignals,expnoectedexpforerimenmoleculestsat
athebreducedoostingreservonoitherpressureelectrode-vof0.01oltagembardepwereendencepwerformed,ouldbewhereexpnoected.strongeffectof

4.4Electrode-voltagedependence

61

AsshowninFig.4.9,theelectrode-voltagedependenceofthemoleculesignalsis
welldescribedbythecalculationsovermorethantwoordersofmagnitude.This
excellentagreementbetweenexperimentandtheoryverifiesthatthefilteringpro-
cessiswelldescribedbythemodelofelectrostaticvelocityfilteringpresentedin
section2.1,usingtheStarkshiftsofthewaterisotopologscalculatedinsection4.1
anddeducingthetotalguidedfluxfromthecontributionsofthedifferentinternal
statesasdiscussedinsection4.2.
HDOshowsthelargestmoleculesignalofallthreewaterisotopologs,aspredicted
fromcalculations.ExperimentallyaratioofdetectorsignalsbetweenHDOand
D2Oof16.4(18.9)isdeterminedataguidingfieldof130(100)kV/cm,wherethe
calculationspredict14.7(20.5).Thisiswellwithintheoveralluncertaintygivene.g.
bythedeterminationoftherelativecontributionsofisotopologsinjectedthrough
thenozzleasderivedfromtheresidual-gas-analyzersignal.Themeasurementsdone
withdifferentHDOamountsgivecountratesagreeingtowithin5–10%,whichal-
lowsanestimatefortheuncertaintyoftheresidual-gas-analyzercorrectionsapplied.
Furthermore,theguidedfluxofHDOlargelystemsfromrotationalstatesathigher
rotationalenergies.Thesearethereforemorestronglyaffectedbycentrifugaldistor-
tioncorrectionsnotincludedintherigidrotorapproximationbeingused,leadingto
energylevelshiftsandhencechangesofStarkshiftswhichcanaffecttheaccuracy
.scalculationtheofThemeasuredsignalsofguidedH2OandD2Oshowaquarticdependenceonthe
appliedelectrodevoltage,aswasshownforD2Oalreadyinapreviousexperiment
[Rie06].Theelectrode-voltagedependenceforthemoleculesignalofHDOisbest
describedbyaquadraticbehavior,confirmingthemaincontributionsfromstates
withlinearStarkshiftspredictedbycalculations.Thisdifferentdependenceofthe
guidedsignalontheappliedelectricfieldisdirectlyevidentfromdifferentslopesin
thedoublelogarithmicplotshowninFig.4.9.
Thedetectorsignalsofthewaterisotopologscanberoughlycomparedtoother
moleculesusedsofar.FordeuteratedammoniaND3,countratesontheorder
of3×105counts/swereobservedinthesamesetupatanelectrodevoltageof
±5kV,usingareservoirpressureof0.1mbarwiththenozzleassemblyatroom
temperature.WiththeQMSusedintheexperiment,ND3isdetectedatmass
20amuwithafragmentationprobabilityof53%.Therefore,onearrivesatatotal
signalofguidedND3moleculesof6×105counts/s.Whena1:1mixtureofH2O
andD2Oispreparedandareservoirpressureof0.1mbarismaintained,asignalof
1.5×104counts/sforguidedHDOmoleculesisobservedatmass19amu.Here,a
fragmentationprobabilityof74%fordetectionatmass19amumustbetakeninto
account,aswellasthepurityof≈48%forHDOinjectedthroughthenozzleintothe
guide.Puttingalltogether,thisresultsinatotalsignalof4×104counts/sforHDO,
assumingthesamenumberofmoleculeswereinjectedintotheguide.Thereasonfor
thissmallerfluxcanbefoundinthefactthatforHDOonlyfewstatesexhibitlinear
Starkshiftsandhencecontributetotheguidedflux,whereasND3exhibitsmainly
linearStarkshifts.FurthermoretheStarkshiftsofHDOaresmallerduetothe

62

Coldguidedbeamsofwaterisotopologs

Figure4.10:NormalizedvelocitydistributionsforthewaterisotopologsH2O,D2O,and
HDOatanelectrodevoltageof±5kV.Thevelocitydistributionsarederivedfromthe
risingslopeoftime-of-flightmeasurementssuchastheoneshowninFig.4.8.Thesolid
curvesareaguidetotheeye.Verticalarrowsindicatethecutoffvelocitiesobtainedby
linearextrapolation(dashedlines)ofthehigh-velocityside.

smallerdipole-momentcomponentalongthea-axis(0.66Db[Bri72])ascompared
tothedipolemomentofND3(1.5Db[Hal67,DL81,Gan87]).Nevertheless,thefact
thatmoleculeswithsodifferentStark-shiftpropertiescanbeefficientlyfilteredoutof
athermalgasillustratesthewideapplicabilityofthevelocity-filteringtechnique.For
chemicallystablepolarmoleculeswhichcanbesuppliedtothenozzleviatheTeflon
tube,itissufficienttobringthemintothegasphaseinareservoiratapressurein
the0.1–1mbarrange.Atsmallerpressuresguidingisstillpossible,howeveratthe
expenseofreducedsignals.Chemicallyveryreactivemoleculessuchasmolecular
radicals(typicalexamplesareOHandNH)areinprinciplealsoguidable.Beams
ofmolecularradicalscanbeloadedintoabuffer-gascell,wheretheythermalizeby
collisionswiththecryogenicheliumgas[Cam07].Thetranslationallyandinternally
cooleddownmoleculescanthenbeextractedbyanelectrostaticquadrupoleor
magneticguide[Pat07,Som09,vB09]andmadeavailableforfurtherexperiments.

4.5Velocitydistributions

ThetratedbdifferenytheirtveloStark-shiftcitypropdistributions.ertiesofThtheevacutoffriousvweloatercity,i.isotope.,theologsveloarecityalsoofillus-the
givfastestenbythemoleculesratiobwhicetwheencanthestillbemolecules’guidedmassaroundanditsthebStarkendsshift.oftheHence,quadrupitdepole,endsis
ontherotationalstateofthemolecule.Sinceformoleculesfromathermalsource
withmanythestateslargestconStarktributetoshift.theInguidedtheexpflux,ertimenhet,cutoffthevelocutoffcityveloiscitgivyenisbythedeterminedstate
fromalinearextrapolationofthehigh-velocitysideofthevelocitydistributionto-

4.5Velocitydistributions

63

electroFiguredev4.11:oltage(±3NormalizedkV,±5vkV,elocit±7ydkV).TheistributionssolidforcurvD2esOareandaHDOguidetoasatheeyfunctione.Theof
vtionertical(dashedarrowslines)indicatetothethehigh-vcutoffelovceloitycityside.,whichisdeterminedfromalinearapproxima-

wardszero.Fromthemeasurementsperformedatanelectrodevoltageof±5kVit
canbeseeninFig.4.10thatthemaximumofthedistributionaswellasthecutoff
velocityshiftstowardshighervelocitiesfromH2OtoD2OandHDO.Thisiscaused
bythemuchlargerStarkshiftsofHDOascomparedtoH2OandD2O(seeFig.4.4).
ThewidevelocitydistributionforHDOiscausedbythelargeStarkshiftsfound
forthisisotopologandbytheusedbendradiusof5cm.Experimentally,cutoff
vateloancitieselectroof60devm/soltagforeHof2O,±569kV.m/sforCalculatedD2O,Sandtark130shiftsm/sofforstatesHDOconaretributingdeterminedto
theguidedflux(similartoTbl.4.8,butforaguidingfieldof93kV/cmreachedat
±5kVelectrodevoltage)resultincutoffvelocitiesof57m/sforH2O,67m/sforD2O
andHDO125statesm/sforwithHDO.largeStarkTheseareshiftsinofgoupodto0.80agreemencmt−1watith±5thekVelectromeasuremendevts.oltageFor
arepredictedtocontribute≈20%totheguidedflux.Thesestatesmightbere-
sponsibleforthesmallbutnon-zerosignalintheHDOvelocitydistributionbetween
130m/sand150m/s,beingsupported−1bythefactthatacutoffvelocityof150m/s
correspondstoaStarkshiftof0.80cm.Notethatthissignalexceedingthelinear
extrapolationtothefallingslopeofthevelocitydistributionispresentinallthree
velocitydistributionsofHDOshowninFig.4.11(b).Onthelow-velocitysideofthe
velocitydistributionalinearextrapolationdoesnotcutthehorizontalaxisatzero
velocity.Thiscanbeattributedtocollisionsofthemoleculesinthevicinityofthe
effusivesource,whichremovestheslowestmoleculesfromthethermaldistribution.
Thiseffectivelyleadstoaboostingofthemoleculesenteringtheguideandhenceto
ashiftofthevelocitydistribution,asexplainedinchapter3.
Measurementsofvelocitydistributionsfordifferentelectrodevoltages(±3kV,
±5kV,±7kV)wereperformedforD2OandHDO,andareshowninFig.4.11.In
thedata,ashiftofthemaximumofthedistributionandofthecutoffvelocity,i.e.,

64

Coldguidedbeamsofwaterisotopologs

ForFigureD2O4.12:thesolidVoltagelinedeprepresenendencetsaoflinearthefit,longituwhiledinalforcutoffHDOvtheelocitsolidyforcurvD2eOisaandfitHDofO.a
square-rootdependence.Thesedependenciesareexpectedforquadratic(D2O)andlinear
(HDO)Starkshiftsrespectively.

themaximalvelocityofmoleculeswhichcanstillbeguided,canbeseen.This
istobeexpected,sincelargervoltagesappliedtotheguideelectrodesresultina
deepertrappingpotential.Hence,fastermoleculesareguided.Thedependenceof
thecutoffvelocitiesontheappliedelectrodevoltageisshowninFig.4.12.Alinear
dependenceinthecaseofD2Oandasquare-rootdependenceinthecaseofHDOis
observed.Aswasshowninsection2.1,thecutoffvelocitydependsonthesquare-
rootoftheStarkshiftattheappliedguidingfield.Hence,alineardependencesuch
astheoneobservedforD2OisfoundformoleculeswithonlyquadraticStarkshifts,
whereasasquare-rootdependenceisfoundformoleculessuchasHDOwherestates
withlinearStarkshiftsdominatethefluxofguidedmolecules.

Summary4.6Coldefficientguidedwaybbyeamsofelectrostaticthewvaterelocitisotopyolfiltering.ogsH2O,TheD2O,signalsandoftheHDOaredifferenprotducedisotopinologsan
showquarticandquadraticelectrode-voltagedependencies,respectively,causedby
conquadratictributingStarkmosttoshiftstheforHguided2OfluxandinD2O,HDO.andbTheseylineardifferenStarktshiftStark-shifsoftthepropertiesstates
arealsoevidentfromthedependenceofthecutoffvelocityontheappliedguiding
electricfieldasmeasuredforD2OandHDO.
iorFoforathetheoreticalmoleculesinandescription,externaltheelectinfluencericoffieldismolecularinvestigated.parametersMoreonspthebecificallyehav-,
themagnitudeoftherotationalconstantsandtheorientationoftheelectricdipole
BasedmomentonwitthishrespdiscussionecttoofthemolecularrotationalStarkaxesshifts,determinespredictionstheformolecules’theStarkefficienciesshift.of

4.6Summary

65

electrostaticvelocityfilteringforthedifferentisotopologsaremade.Excellentagree-
menguidedtbetwmoleculeeenthesisexpfound,erimentallyconfirmingobservthatedthesignalsvelocitandthey-filteringcalculationsprocessofiswfluxesellde-of
scribedbythepresentedmodel.Furthermore,thesecalculationsallowtodeduce
pas80%opulationsinofthecaseindividualofH2Orotationalforarostatesom-tempinthegeratureuidedbsource.eam,Inwhicthehcannextbecashapter,high
aanddirectappliedmethtoodcoldforinguidedbternal-stateeamsofdiagnostics,formaldehydedepletionmoleculessp[ectroscopMot07].y,isdescribed

66

Cold

guided

b

eams

of

aterw

isotop

logso

5Chapter

ybthermometryternal-stateIndepletionspectroscopyinacold
guidedbeamofformaldehyde

Inthischapter,anexperimentaltoolformeasurementsoftheinternal-statedistri-
butioninguidedbeamsofpolarmoleculesispresented.Intheexperimentswith
thedifferentwaterisotopologsdiscussedinchapter4,thisinternal-statedistribution
couldbeinferredonlyindirectlyfromthespecificelectrode-voltagedependenceof
thesignalofguidedmoleculesaswellasfromtheirvelocitydistributions.Thesedata
yieldedinformationabouttheStark-shiftcharacteroftheinternalstatesdominating
molecules.guidedoffluxtheComplementingelectrostaticguidingbydepletionspectroscopy,theinternal-state
accessible.distributionFoformaldehelectrostaticallydeexhibitsyaguidedricformaldehh-structuredyde(Helectronic2CO)spectrummoleculesinisthedirecnear-tly
ultraviolet(280–360nm)region[Can90,Mot08],permittingdirectexcitationwith
narrow-bandwidthcw-lasers.Themoleculesareexcitedinthe201403rovibrational
bandoftheA˜1A2←X˜1A1transitionaround330nm[Clo83].SincetheA˜1A2
excitedstateofformaldehydepredissociates[Moo83],moleculespumpedtothis
statearelostfromtheguidedbeam.Hence,thedepletioninducedbythelaser
beamisadirectmeasureforthepopulationofastate,evenwhenonlytheintegrated
signalisaccessibletothedetector.Byaddressingindividualrotationalstates,the
internal-statedistributionoftheguidedformaldehydemoleculesisinferredandcan
becomparedtotheoreticalpredictions.
Insection5.1,theexperimentalsetupusedfortheseexperimentsispresented.
Here,mainlythecontinuous-wavelasersysteminthenear-ultravioletspectralre-
gionisdescribed.Asaprerequisitefordepletionspectroscopy,thetransitionfre-
quenciesfromthestatesofinterestintheguidedbeamareneeded.Therefore,
room-temperatureabsorptionspectroscopyofformaldehydeinthewavelengthrange
30140–30790cm−1,coveringtworovibrationalbands(201403and202401),hasbeenper-
formed[Mot08].Therotationalconstantsderivedfromafittothisdatausinggenetic

67

68

Internal-statethermometrybydepletionspectroscopy

Figure5.1:Experimentalsetup.Formaldehydemoleculesfromaneffusivesourceare
injectedintotheelectrostaticquadrupoleguideandledtotheQMScross-beamionization
volume.Theultraviolet(UV)laserbeamisoverlappedwiththemolecularbeaminthe
last15cmlongstraightsectionoftheguide.Thelightisswitchedonandoffbyanelectro-
opticalmodulator(EOM)placedbetweentwopolarizingbeamsplittercubes(PBS).

algorithms[Mee04,Mee06a,Mee06b]isthenusedforcalculationsofthespectrum,
allowinglineidentificationandpredictionoflinepositionsforguidedstates.Insec-
tion5.2thisroom-temperaturespectroscopyexperimentisdiscussed.Theactual
expguidederimentformaldehtoydedeterminebeamisstatepodiscussedpulationsinbsectionyde5.3.pletionThere,sptheectroscopmeasureyinmenthetscoldare
alsocomparedtotheexpectedcontributionsofindividualinternalstatescalculated
bcoyolingtheofprothecedurereservdescriboiredindeedfortheincreaseswatertheisotoppuritologsyofinthechapterguided4.bTeamoshowdepletionthat
spectroscopywasperformedforsourcetemperaturesrangingfrom150–300K.

setuptalerimenExp5.1TheexperimentalsetupisshowninFig.5.1.Gaseousformaldehyde(H2CO)is
producedbyheatingparaformaldehydepowder(Sigma-Aldrich)toatemperature
of80–90◦C.Tocleanthedissociationproductsandremoveunwantedwater◦and
[pSpe35olymer].Therests,theformaldehgasisydeledgasthroughisthenadry-iceinjectedcoldintotraptheataquadrutemppoleeratureguideof≈throug-80hC
theceramicnozzledescribedinsection2.2.Thetemperatureoftheliquid-nitrogen
cotempolederaturesnozzlebcanetwbeeenvaried150–300inthKecanrangebe100–300usedtoKbmainyatainheater.areasonableSimilartopressureammonia,of
formaldehydeatthenozzle.Forlowertemperaturesthevaporpressureistoosmall,
suchthatnousefulmoleculefluxoutofthenozzleintotheguideisachievedanymore.
Theslowmoleculesareguidedaroundtwo50mmradiusbendsandthroughtwo
spdifferenectrometertialpumping(QMS)instagesthetosamethesetupcross-baseamdiscussedionizationinunitsectionof2.2a.Inquadruptheolestraighmasst

5.1Experimentalsetup

69

inFigurethe3305.2:nmwaLaservelengthsetup.Trangeunable,ispronarroducedbyw-bandwidth,second-harmoniccontinuous-wgenerationave(cw)ofthelaseroutputlight
ofaringdyelaser.Forwavelengthcontrol,asmallpartofthefundamentaliscoupledinto
Perotsingle-moindeterferometer.opticalfibAersBBOandsencrystalttoisawplacedavinemeterthefocus(HighFinesseofanenhWS7)anceandmenttocaavitFyabry-for
thefundamental.Toachievephasematchingbetweenthefundamentalandthesecond-
harmonicradiation,theangleofthecrystalrelativetothepropagationdirectionofthe
laserlightisadjusted.Theresonancefrequencyoftheenhancementcavityislockedto
thefrequencyofthefundamentalbytheH¨ansch-Couillaudmethod[H¨an80].Sincethe
beam-pointingoftheproducedUVlightvarieswithwavelength,twoCCDcamerasare
usedtomonitorthebeamposition.Abeam-pointingdeviationfromthereferenceisthen
correctedwithtwosteeringmirrors(SM).Toobtainahigh-qualityGaussianbeamprofile,
whichcanbeproperlyalignedthroughtheguide,thelightissentthroughtwocylindrical
lensesforastigmatismcompensationandmodecleanedbyapinhole.

withsectionthebeforeguidedtheQMSmolecularbionizationeamovuniterathelengthultraofviolet≈15(UV)cm.laserbeamisoverlapped
Thecontinuous-wave(cw)narrow-bandwidthtunableUVlaserlightiscreatedby
second-harmonicgenerationoflightfromaringdyelaserinanexternalenhancement
cavity.Thedyelaserislockedtoatemperature-stabilizedreferencecavityandits
outputfrequencyismonitoredbyawavemeter.Aschematicofthelasersetupis
shoopticalwninmoFig.dulator,5.2.aroundAfterb100eammWshapinglaserlighandtatlaserawpaovwelenergthswitcofhing330bnmyisanavelectro-ailable
fortheexperiment.Thelaserbeamisfocussedintotheguidecounter-propagating
oftheUVmolecules.lightonThethebeamhigh-vwaistoltageofelectro150–200des,µmwhicishopwtimizedouldleadfortominimalapressurescatteringrise
andconsequentlyanincreaseinbackgroundcountrate.Aftercarefulalignmentno
simsignificanulationstofinfluentheceofmotiontheofUVmollighteculesoninthetheQMStrappingcountfieldrateshoiswaobservted.ypicalNumericaldiameter

70

Internal-statethermometrybydepletionspectroscopy

ofthemoleculesguidedtobpasseamofthrough≈0.8themm,laserindepbeamendenonttheiroftheorbit.rotationalstate,causingmost

5.2Room-temperatureabsorptionspectroscopyof
ydeformaldehTheultravioletspectrumofformaldehyde(H2CO)hasbeenextensivelyinvestigated
alreadyaroundthebirthofmolecularspectroscopy[Die34].Asoneofthesimplest
polyatomicmoleculesitcanbeconsideredamodelsystemformolecularphysics.
Avarietyofstudieshasbeencarriedouttoexperimentallydeterminekeyparame-
tersforformaldehydephotochemistrysuchasphotodissociationquantumyieldsand
absoluteabsorptioncrosssections.Thesenumbersarerelevantforatmosphericsci-
ence,forwhichformaldehydeisanimportantmolecule.Formaldehydeispresentin
theatmosphereatconcentrationof∼50pptv(partspertrillionbyvolume)inclean
troposphericair[Rie99]andupto10–70ppbv(partsperbillionbyvolume)inthe
airinurbancenters[Gro83,Wil96].ByexcitationoftheA˜1A2←X˜1A1transition
inthe260–360nmwavelengthrangetwodissociationchannels[Moo83,Bow06]with
highquantumyields[McQ69,Cla78,Hor78a,Hor78b,Rei78,Moo78]areopen:
H2CO+hν→H2+CO(5.1a)
H2CO+hν→H+HCO(5.1b)
Thereactionchannel(5.1a)opensatwavelengths<360nm,andthereactionchan-
nel(5.1b)opensatwavelengths<330nm.Thereactionproductscanthenfurther
reactwithotherspeciespresentintheEarth’satmosphere.ThisUV-light-induced
dissociationisusedforthedepletionspectroscopy,sinceitoffersaninternal-state-
dependentlossmechanismforguidedformaldehydemolecules.

5.2.1Formaldehyde-spectroscopysetup
Theexperimentalsetupusedfortheabsorption-spectroscopymeasurementsisstan-
dard[Dem03a].However,duetothesmallabsorptioncrosssectionsofformaldehyde
(σ∼10−19cm2),measurementsmustbeperformedatrelativelyhighdensitiesand
twlongoopticalsphericalpathUVlengths.mirrorsAsplacedshownoutsidineFig.the5.3v,aacuumchome-madehambermandultipassonesetupadditionalusing
retroreflectionmirrorwasused.

Vacuum-chambersetup
Connectedtothevacuumchamberareaturbomolecularpump,apressuregauge
(PfeifferVacuum,CompactFullRangeGaugePKR261),aflowvalveforformalde-
hydeinput,andaflowvalveallowinganalysisofthechamber’scontentsbya
residual-gasanalyzer(PfeifferVacuum,PrismaQMS200).Theeffectivepumping

5.2Room-temperatureabsorptionspectroscopyofformaldehyde

71

Figure5.3:Room-temperatureabsorption-spectroscopysetup.Aformaldehydepressure
of50Paismaintainedinthevacuumchamberwhichisusedasanabsorptioncell.To
achievealarge(≈3.15m)opticalpathlength,amultipass,retroreflectionconfigurationis
utilized.Forthatpurpose,curvedmirrorsrefocusthebeamintothespectroscopychamber
inacavity-likemanner.Anadditionalcurvedmirrorisusedforretroreflection.Before
beingmodematchedintothe“cavity”,partoftheUVlightissplitoffbyafused-silica
wedgeanddirectedonaUV-sensitiveSiphotodiodeservingasalaserpowerreference
(ref.PD).Toobtaintheabsorptionsignal,thesamefused-silicawedgesendsapartof
thebackreflectedlightonanotherphotodiode(abs.PD).Anelectro-opticalmodulator
(EOM)canbeplacedinthebackreflectedbeamforDoppler-freefrequency-modulation
spectroscopy[Zep07].

tspweeneedofthetherecipienturbtoandmolecularthepumppumptoacanvoidbeexcessreducedbpumpingyanofanglevformaldehalveyde.placedWithbe-
theturbo−6molecularpumpthespectroscopychamberisevacuatedtoabasepressure
inthe10mbarrange.
(seeGaseoussection5.1)formaldeh.SinceydeisprformaldeheparedydethemolecusameleswaydissoasforciatetheuponguidingUVexpexcitation,erimentsa
stableflowofformaldehydeismaintainedbyslightlyopeningthevalvebetween
theturbopumpandthevacuumchamber.Thepartialpressuresofformaldehyde
anditsdissociationproductsaremonitoredwiththeresidual-gasanalyzerandthe
formaldehoptimizedydeforainputconstanflowtrateratio.asThiswellwaasytheflomeasuremenwtothetsareturbpoerformedmolecularatapumpconstanaret
formaldehydeconcentration.Intheexperimentaconstantpressureof50Pa(=
5×10−2mbar)ismaintainedinthevacuumchamber,withaformaldehydefraction
estimatedtobe≥50%.

Opticalsetup,detectionoftheabsorptionsignal,andlaser-frequency
tuningToachievealargeopticalpathlengthinarelativelycompactsetup,amultipass
andretroreflectionconfigurationisused.TheUVlaserbeamisinitiallyfocussed
intothevacuumchamberwiththebeamparametersmode-matchedtotheeffective
cavitymodegeneratedbythetwomultipassmirrors.Twocurvedmirrorswitha
intoradiustheofvcurvacuumaturecham(RoC)ber,ofallo200wingmm7outsidepasses.theAllvcurvacuumedcmirrorshamberarerefopcusositionedthebsuceamh

72

Internal-statethermometrybydepletionspectroscopy

thattheirradiusofcurvaturematchestheGaussianmodeleavingthespectroscopy
lengthsetup.canByevanenbeadditionaldoubled,yieldingretroreflection≈3.15mirrormina(RoCcompact=500≈mm),22.5cmthelengtheffectivveacuumpath
er.bhamcpicForkingupdetectionpartofathefused-silicaoriginalbweamedgeisusedasplacedpowernearnreferenceormalandincidencepartofwhicthehalloretrore-ws
flectedbeamcontainingtheabsorptionsignal.Thepicked-upbeamsarefocussed
onTotuneUV-sensitivtheelaserSiphotofrequencydio,desalinear(ThorlabsvoltagePDrampA36EC).isappliedtotheexternalscan
inputfundamenofthetaldywithealaser.scanspTherebeedyof,≈the45laserGHz/s.Ffrequencyoreacishofswepttheseovswereeps20GHzthecenintralthe
sweep,frequencygivingoftheagreemenfundamenttalwithinis0.001measuredcm−1withinthethewavfundamenemetertabl.eforeForandaftercalibrationthe
ofthescanspeed,thetransmissionsignalofaFabry-Perotinterferometer(FPI)
is10GHzrecorded.intheSubseqfundamenuenttal,scansgivingare50p%oerformedverlapwithforacenconcatenatintral-frequencygindividualdifferencesweeps.of

analysisdataandacquisitionDataAfour-channeldigitaloscilloscopeisusedfordataacquisition.Simultaneously,the
externalramp,theFPItransmissionpeaks,thereferenceandabsorptionphotodi-
odesignalsarerecorded.Forlaterdataanalysisthechannelsarerebinnedtoa
resolutionof100MHzintheUV,whichwaschosensuchthatindividualrotational
transitions,whichareDoppler-broadenedto2.4GHz,arewellresolved.Overlap-
pingadjacentscansusingthecentralfrequenciesmeasuredwiththewavemetershow
goodoverlapbetweenlinespresentinbothscansandconfirmthecentralwavelength
measurementswiththewavemeter.

ModificationsforDoppler-freemeasurements
TheexperimentalsetupusedforDoppler-freemeasurementsandthedevelopedana-
Zepplyticalenfeldmodeletforal.[theZep07].amplitudeHereofonlytheDoppler-frmoeepdificationseaksistodescribthespedinectroscopdetailybysetupMartinare
summarized.ToeasethedetectionofweakDoppler-freesignals,frequencymodu-
lation(FM)spectroscopy[Bjo80,Bjo83]isperformed.Forthisanelectro-optical
modulator(EOM,LeysopEM400K),resonantlydrivenwithafrequencyof15.8MHz
forthecreationofsidebands,isplacedintheretroreflectedbeam(seeFig.5.3).Since
ademodulationofthesignalat15.8MHzisnecessary,fastphotodiodeswithasuf-
ficientlyhighbandwidthareusedfordetection(ThorlabsPDA155).Furthermore,
sincetheA˜1A2←X˜1A1electronictransitionsinformaldehydeareweak,highlaser
powersareneededtoreachasignificantsaturationanddiscriminatetheLambdips
tem,againstUVthelaserpowersDoppler-broadenedof250–350bacmWkground.areavailableAfterforcarefulthetuningsaturation-spofthelaseectroscoprsys-y
t.erimenexp

5.2Room-temperatureabsorptionspectroscopyofformaldehyde

73

discussionandResults5.2.21˜1˜aimedPreviousatthemeasuremendetermtsinationoftheofAA2absolute←XtempA1roerature-depvibrationalendenbandtofabsorptionformaldehcrossyde
dissosectionsciation[Can90pro,cePssesop05,folloSmi06wing].theOtherUVexpexcitationeriments[studiMcQ69ed,theCla78quan,tumHor78a,yieldofHor78bthe,
forRei78the,Moo78description].Theseofcrossphotocsectionshemistryandinquanthetumatmosphereyieldsareinducedimportanbyttheparameterssunlight
asdiscussedintheintroduction.Thesemeasurementshavebeenperformedusing
eitherbroadbandlightsourcesandspectrometers([Can90]andreferencestherein)
withr−1esolutionsabove1cm−1orpulsedlaserswithspectralresolutionsof,e.g.,
et0.35al.cm[Co05[P]op05with,aSmi06].resolutionAnofexception0.027cmto−1,thisarespanningthethemeasuremelongwanvtsbyelengthD.T.rangeCo
2241(351–356ronm)vibrationalofthebandA˜1Ab2y←M.X˜1ScAh1ulz[band,Sch04and].theExceptformeasurementhesetstwofotheexp2014erimen01andts
00therotationalresolutionlinesofwithapreviousDopplermeasuremenwidthofts2.4isnotGHzathighroomenoughtemptoerature.resolveindividual

studiesprevioustoComparisonTheimprovementinresolutioncomparedtopreviousstudies[Smi06]witharesolu-
tionof0.35cm−1isshowninFig.5.4,wheretheregionaroundthebandheads
oftherRKa=3progressionat≈30389cm−1andtherRKa=4progressionat
≈30397cm−1withmanylinesclosetogetherareshown.Individualrotationallines
arewellresolvedandaccuratelinepositionsaswellasintensitiescanbedetermined.
Forthe−1figuresshownthemeasureddataisbinnedtoaresolutionof100MHz=
0.003cmwhichissufficienttoresolvetheDoppler-broadenedlines.
C.A.Smithetal.[Smi06]usedalineshapefunctionwithafullwidthathalf
maximum(FWHM)of0.45cm−1toreproducetheirmeasuredspectrafromsimula-
tions.ThiswassurprisingsincetheUVlinewidthoftheirlasersourceswasexpected
tobe≤0.20cm−1ascalculatedfromthemeasuredlinewidthofthefundamental.
Itwasspeculatedthatthiscouldeitherbeexplainedbyextremelyshortexcited
statelifetimesnotinagreementwithliteraturevalues[Moo83]orbyanadditional
technicalbroadening.Fromourdataawidthof2.4GHzFWHMisdeterminedfor
isolatedlinesacrossthewholefrequencyrange,beingingoodagreementwitha
Doppler-broadenedlineprofileatroomtemperature(293K).Therefore,theseex-
tremelyshortlifetimescanberuledout,andtheirassumptionofalargerlaser
ed.confirmislinewidth

Fitofthe201403and202401rovibrationalband
Forthefitofthemolecularparameterstotheexperimentalspectrum,Watson’s
tortionA-reducedtermshasHamiltonianbeen[Wusedat67,withWaat68]geneticincludingalgorithmquartic(GA)andassexticoptimizer.centrifugalDetailsdis-

74

Internal-statethermometrybydepletionspectroscopy

Figure5.4:Comparisoninresolutionofourabsorptiondata(top)topreviousmeasure-
ments(bottom).ThemeasurementsbyC.A.Smithetal.[Smi06]withtheso-farreported
withhighestmanyresolutionlinescloseinthistogether,wavconelengthvergingrangetoarethechosenbandheadsasofreference.therRAKawa=v3elengthprogressionrange
at≈30389cm−1andrRKa=4progressionat≈30397cm−1,wasselectedtoshowhow
individuallinescanberesolvednow.ThedataofC.A.Smithetal.areoffsetby0.5for
.yclarit

abouttheGAandthecostfunctionusedforevaluationofthequalityofthefitcan
befoundinRefs.[Mee04,Mee06b,Mee06a].Table5.1compilestheso-determined
parametersandcomparesthemtothepreviousparametersforthegroundstate
[Clo83]andtheexcitedvibronicstates[Smi06].Theground-stateparametersare
inexcellentagreementwiththevaluesthathavebeendeducedfrommicrowavefre-
quenciesandcombinationdifferencesininfraredandelectronicspectra,weightedby
appropriatefactors[Clo83].Theparametersforthe201403and202401vibronicbands
arecomparedtothevaluesgivenbyC.A.Smithetal..Toimprovethequality
ofthefit,theexperimentaldataabove30390cm−1havebeenexcludedfromthefit
ofthe201403vibronicband,sincestrongperturbationsofthelinepositionsbetween
30390and30404cm−1wereobserved.Thereasonwhyexclusionofapartofthe
datawasnecessarymightbeaninterferencewiththeweakvibronic201401601band
withitsoriginat30395cm−1.Althoughthisbandwasincludedwiththemolecular
parametersfrom[Ape85]asstartingvaluesinourfit,noimprovementofthecost
functioncouldbeobtainedbythiscombinedfit.Duetothehightemperature,high
J-statesarepopulatedandsexticcentrifugaldistortiontermsinthefithaveshown
tobenecessary.Theappropriatenuclearspinstatistics(Kaevenlevels=1;Kaodd
levels=3)havebeentakenintoaccount.Forcomparison,partsofthesimulated
andthemeasuredabsorptionspectrumaroundthebandoriginareshowninFig.5.5.

5.2

tureera-tempomRo

Figure(inlation

5.5:erted,v(in

absorption

Comparisonottom)berted,

wetbeenthearound

yectroscopsp

theoriginthe

measuredtheoforigin

of

ydealdehform

lationFigure(inv5.5:erted,bComparisonottom)betaroundweenthetheoriginmeasuredofthe201403absorptionvibrational

ectrumspbandvibrational

(top)30340.08atband

and30340.08

the30340.08

vibrationalbandat30340.08

75

u-sim1−cm.

cm

76Internal-statethermometrybydepletionspectroscopy
Table5.1:MolecularparametersofthegroundstateandtheA˜1excitedstateofformalde-
hydefromaGA-Fitofthe201403and202401vibronicbands.AllvaluesaregiveninMHz.
GA-Fit201403GA-Fit202401Ref.[Clo83]201403Ref.[Smi06]202401Ref.[Smi06]
AB281970.85(27)38836.53(27)3281971.44(43)8836.14(25)238836.0455(1381970.572(24))----
C103DJ34002.67(16)75.38(7)34002.57(25)75.61(11)34002.2034(1275.295(21))----
101033DDJKK1290.24(20)19424.6(6)1290.00(29)19424.1(6)19423(7)1290.50(37)----
103dJ9.85(24)10.30(25)10.4567(9)--
101093dHKJ1028.39(60)33.5(16)1027.68(66)34.1(20)31(21)1026.03(25)----
101099HHJKJK-112184(3)29021(1)2-112179(3)9022(1)-112000(280000)29019(690)----
101099hHJK4470000(2500)45.3(14)4470000(4100)40.1(9)4542.3(17)00000(200000)----
101099hhJKK1372119.6(24)15592(5)11372119.5(36)5612(6)1372000(18000)15665(310)----
νA0909572633(41)246402.8(40)2919120592(48)59111.6(43)--909246669(90)571763(1110)919259090(21)120745(690)
B33158.0(19)32952.3(33)-33194(21)32918(16)
C103DJ30268.8(23)145.9(44)29764.4(39)89.6(9)--188(17)30277(21)2999(12)837(14)
101033DDJKK-43024(63)3204(52)19474(98)617(14)---48234886(450)7(1919)9383(33)1484(45)
101033ddJK16350(700)-9.8(40)123.1(27)90(380)--11892(44949(14)7)-6110(12)75(959)
101099HHJJK-20000(12000)6480(9970)30000(5400)16(18)------
109HKJ150000(80000)158000(88000)---
101099hHJK8770000(620000)-24100(8500)3240000(640000)51(12)------
101099hhJKK3130000(490000)28100(2100)114200490000(107000)(6200)------

5.3Internal-statedistributionofguidedformaldehydemolecules

77

RotationalstateΔWspSpG
|J,τ,M(cm−1)(%)(%)
|3,3,32.860.2528.52
||14,,12,,141.292.280.5310.2303.624.93
|3,3,21.820.2523.46
|2,2,22.420.1343.22
|5,1,51.900.2053.05
Table5.2:Propertiesofselectedrotationalsstates|J,τ,Mofformaldehydewithapop-
ulation≥3%intheguidedbeam.ΔW:CalculatedStarkshiftatanelectricfieldof
P100opulationkV/cm.inpS:theguidThermaledpbeamopulationatanintheappliedeffusivtrappiengsourceelectricatatempfieldoferatu100reofkV/cm.150K.pNoteG:
conthetributionincreaseofinptheopusourcelationbofyathesefactorofrotational10to35.statesintheguidedbeamrelativetotheir

5.3Internal-statedistributionofguidedformalde-
moleculesydehpTheopulationinternal-statintheeeffusivedistributionsource,ofincludingguidednmoleculesuclearspinisstatistics,determinedandbybythethethermalStark
shiftisotopofologstheinrotationalsection4.2states.Finortheformaldehappliedyde,guidingwhichfields,isasalsoanexplainedasymmetricforthewrotor,ater
theStarkshiftΔWscanbecalculatedthesamewayasdescribedforthewater
isotopologsinsection4.1.Themeasurementswithformaldehydeareperformed
withareservoirpressureof0.1mbar,i.e.,inthemediumpressureregime,sameas
forthewaterisotopologs.Atthisintermediatepressuresetting,thecontribution
oftheasquarerotatiofonalitsstateStark|J,enτ,Mergyto(ΔWthes(Esignal))2ofatguidedthemaximalmoleculesistrappingpropfieldortionalEto.
maxmaxTherotationalStarkstatesshiftsinatathetguideypicalaretrappinlistedginfieldTbl.of5.2100fortkV/cmhoseandstatesthewhicphconopulationstributeof
morethan3%tothetotalfluxatasourcetemperatureof150K.

5.3.1Depletionspectroscopyofindividualrotationalstates
Withthedetailedunderstandingoftheformaldeyhdespectrumgainedbytheroom-
temperatureabsorption-spectroscopyexperimentdescribedinsection5.2,individual
rotationalstatesintheguidedbeamareaccessible.Table5.3liststhetransitions
usedtoaddressthehighest-populatedstatesintheguidedbeam.MainlytheR-
branchoutofthe201403vibrationalbandisused,becausethefrequencydifference
betweentransitionsoriginatingfromdifferentinitialstatesissmallestforthisbranch,
allowingeasiertuningofthelaser.UponexcitationwiththeUVlightthemolecules
dissociateandadecreaseintheQMSsignalisdetectedasshowninFig.5.6.Atthe

78

Internal-statethermometrybydepletionspectroscopy

X˜1A1→A˜1A2−1
|J,τ|J,Ka,Kc→|J,Ka,KcFrequency(cm)
|1,1|1,1,0→|2,2,130364.38
|2,2|2,2,0→|3,3,130377.26
|3,3|3,3,0→|4,4,130387.98
|4,2|4,3,1→|5,4,230388.76
|5,1|5,3,2→|5,4,130376.62
|5,5|5,5,0→|6,6,130403.84
Table5.3:Transitionsusedtoaddressthehighest-populatedstatesintheguidedbeam.

Figure5.6:DepletionintheQMSsignalofguidedformaldehydemoleculesatanelectrode
voltageof±1kV.TheUVlightisswitchedonbetween0.5and1.1s.Thelaserlight
istunedtothemaximumofthetransition|3,3,0→|4,4,1atthisguidingelectric
field.Thisfrequencywasdeterminedbyaline-shapemeasurementastheoneshownin
(a).5.7Fig.

wavelengthsof≈330nmusedfortheexperiments,theefficiencyfordissociationis
>90%[Moo83].
Whenscanningthelaserfrequencyaroundthefrequencyofthetransitioninzero
electricfield,anasymmetriclineshapeisobservedasshowninFig.5.7(a).Inthe
guidedbeam,severaleffectsleadtolinebroadeningsandlineshiftsofthedepletion
signal.Sincethemoleculesmovewithatypicalvelocityontheorderof100m/s,
theyexperienceonaverageaDopplershiftof-300MHz.Additionally,thelinesare
broadenedduetothevelocityspreadofthemoleculesintheguidedbeam.However,
themaineffectonthelineshapeoriginatesfromtheradialpositiondependence
ofStarktheshifts.electricTfieldakingexpintoeriencedaccounbtythetheradialmoleculesdistributiandontheoftheresultingmoleculardifferencesbeamin
determinedfromsimulationsandthemeasuredlaserbeamdiameter,thelineshape
canbereproducedasshownbythesolidcurveinFig.5.7(a).Inthediplomathesis

5.3Internal-statedistributionofguidedformaldehydemolecules

79

±5FigurekV.5.7:The(a)solidThecurvetranissaitionfit|to3,3,the0d→ata|4,4,taking1intomeasuredaccounattantheelectrolaserbdeeamvpoltagerofileof
aswellasthedistributionoftheguidedmoleculesintheinhomogeneouselectricfields
presenfrequencytinisthesetsptoecthetroscopmaximyumsection.oftheForcurvtheepoaswer-depindicated.endence(b)Laser-pmeasuremenowerts,depethendencelaser
ofthedepletionsignal.Thelaserfrequencyisfixedtothemaximumofthetransition
|3,3,0→|4,4,1measuredatanelectrodevoltageof±1kV.Thesolidcurveisafit
usingthemodelforΔ(P)describedbyEq.(5.2).

ofMarkusSchenk,theseeffectsarediscussedindetailandmeasurementsforthe
differentaddressedstatesareshown[Sch07a].
Sincetheelectricfieldsinthequadrupoleguidevaryinstrengthanddirection,itis
notpossibletoirradiatethemoleculeswithawell-definedpolarizationwithrespect
totheguidingelectricfield.Ifforagivenstate|J,τmorethanoneMcomponent
contributestothefluxofguidedmolecules,thisleadstoadditionallinebroadening
andmakesitimpossibletodepopulatethedifferentMstatesindependently.Instead,
asignalintegratedoverallguidedMstatesofthestate|J,τismeasured.
Toobtainthesaturateddepletionsignal,whichisameasureforthepopulationof
arotationstate,thelaserfrequencyisfixedtothemaximumofthetransitioninthe
guidingfieldasindicatedinFig.5.7.Then,thelaserpowerisvariedandthevalue
ofthedepletionreachedinthelimitofhighlaserpowerisextractedasshownin
Fig.5.7(b).Toreachsaturationwiththeavailablelaserpower,theelectrodevoltage
issettoarelativelysmallvalueof±1kV,resultinginsmallerlinebroadenings.
Sincetheinteractiontimewiththelaserbeamisvelocitydependent,theabsorption
probabilityforlowlaserintensitiesscalesas1/v.Takingthisvelocity-dependent
absorptionprobabilityintoaccount,thelaser-powerdependenceofthedepletion
vmax,lsignalcanbedescribedby
Δ(P)=N0∙1−0n(v)exp(−αPl/v)dv,(5.2)
whereN0representstherelativepopulationofthespecificstateaddressedbythe
laser,n(v)isthenormalizedlongitudinalvelocitydistribution,Pisthelaserpower,

80

Internal-statethermometrybydepletionspectroscopy

αisatransitionstrengthfactorandlistheinteractionlength.Inthediplomathesis
ofMarkusSchenkdetailedmeasurementsofthelaser-powerdependenceforallthe
addressedtransitionsarepresented[Sch07a].

5.3.2Internal-statedistributionintheguidedbeam
Asdiscussedinsection4.2,thecontributionofindividualinternalstatestothetotal
fluxintheguidedbeamisdeterminedbytheStarkshiftofthespecificstateandits
populationintheeffusivesource.ThepopulationpJτMofarotationalstate|J,τ,M
inthethermalsourcedependsonthesourcetemperatureTas
1EJτM
pJτM=ZgMgIexp−kBT.(5.3)
Here,ZisthepartitionfunctionZ=JτMgMgIexp(−EJτM/kBT),EJτMisthe
rotationalenergy,gMtheMdegeneracyfactorofthestate,andgIthenuclearsspin
degeneracyfactor.ThecontributionofarotationalstatewithStarkshiftΔWJτM
attheappliedtrappingfieldEmaxtothefluxofguidedmoleculesisexpressedas
1fJτM=NpJτM(ΔWJsτM)2,(5.4)
whereNassuresnormalizationofthetotalflux,N=JτMpJτM(ΔWJsτM)2.
Figure5.8(a)showsthecalculatedtemperaturedependenceofthecontribution
ofindividualstates|J,τtotheguidedbeam.Inthisfigure,thepopulationsofthe
individualMstates|J,τ,Mcontributingtoagivenstate|J,τaresummedup,
sincethesearenotresolvedintheexperiment.Asexpected,decreasingthesource
temperatureincreasesthecontributionsoftheindividualrotationalstates,aslong
astheirrotationalenergyissmallerasorcomparabletothesourcetemperature.
Onlyforthestate|5,5,whichhasahighrotationalenergyof241.2cm−1,reduc-
ingthetemperaturedecreasesthepopulationinthethermalsourceandhenceits
contributiontotheguidedbeam.
Theexperimentallydeterminedpopulationofindividualguidedstatesfor±1kV
electrodevoltageareshowninFig.5.8(b).Asameasureforthepopulationofa
rotationalstatethesteady-statevalueofthedepletionsignalobtainedathighlaser
powerisused,asshowninFig.5.7(b).Foreachtemperatureofthesource,thedata
isnormalizedtothestatewithmaximalcontribution,|3,3.Withoutthisnormal-
ization,themeasuredmagnitudeofthedepletionsignalissystematicallylowerby
20%ascomparedtothecalculatedpopulationsoftherotationalstates.Thisvalue
wasfoundtobeindependentoftheaddressedstate.Thisdifferenceisattributed
tomoleculesspiralinginellipticorbitswhichneverbecomeresonantwiththelaser
beamorwhichnevertraversethelaserbeam,andtomoleculeswhichdonotdisso-
ciateandcanstillbeguidedafterdecayingbacktoaguidablestateintheelectronic
groundstate.Byvaryingthetemperaturebetween150and300K,theinternalstate
distributionoftheformaldehydemoleculesaswellastheirvelocitydistributionin

5.3Internal-statedistributionofguidedformaldehydemolecules

81

conFiguretributions5.8:Ttoemptheeraturguidedebdepeam.endenceInthofisthefigupretheopulationsumoinvertheallMstates|statesJ,τistakwithen,largessincet
conthesearetributionnotofresolvindividualedinthestatesexp|J,τerimen,Mt..(a)ThisisinCalculatedcontrastptoopulationTbl.of5.2,whicrotationalhlistsstatesthe
foraguidingelectricfieldof20kV/cm.(b)Experimentallydeterminedandcalculated
p±1kVopulations,electrodevnormalizedoltage,toandtheforptheopulationcalculationsoftheastateguiding|3,3.electricThefielddataofw20kereV/ctakmenwasat
assumed.

thesourceismodified.Fordecreasingsourcetemperature,thereductionofthe
molecules’meanvelocityisdirectlyevidentfromanincreaseinguidedflux.The
goodagreementbetweenthedataandthecalculatedtemperaturedependenceof
theinternalstatedistributionconfirmsthermalizationofthemolecules’rotational
temperatureinthecoolingstageattachedtotheceramicnozzle.Aninteresting
featurevisibleintheexperimentaldataistheincreasingcontributionofthestate
|5,5forhighertemperature.Asalreadydiscussedforthecalculationsshownin
Fig.5.7(a),duetoitshighrotationalenergyof241.2cm−1thisstateislessoccu-
piedatlowtemperaturesascomparedtotheotherstateswhichwerestudied.For
highertemperatures,therelativethermalpopulationofthisstateincreases.Fur-
thermore,thisstatecontributesstronglytotheguidedbeamduetoitsmanyM
stateswithmoderateorevenlargeStarkshifts.
Tocharacterizetheinternalstatedistribution,itwouldbedesirabletousejust
onebasicquantitysuchasatemperature.Findingagooddescriptionoftheinternal
temperatureoftheguidedbeamis,however,non-trivial.Forasourcetemperature
of150Kthemeanrotationalenergyoftheguidedbeamis163.6cm−1,whichis
determinedfromthecalculatedstatepopulations.Thiscorrespondtotheinternal
temperatureofathermalensembleatatemperatureof155K.Themeanrotational
energyis,however,notagoodmeasureforthepurityofthebeam,becausethe

82

Internal-statethermometrybydepletionspectroscopy

filteringTherefore,prothecessguidedreliesonensemthebleisStarkshiftsnon-thermal.oftheinHence,ternalasastatesmeasureoftheforthemolecules.purity
oftheguidedbeamtheentropyS=−pilogpiisdeterminedfromthecalculated
pcomparedopulationstopitheofenalltropyguidedofastates.thermalThisensementropble.yofInthethisguidedcalculationensemblestatesisupthento
J=12areincluded,whichwasfoundtobesufficient.Thetemperature,atwhicha
ofthermaltheguidedgashbaseam.theFsameoraensourcetropy,tempcantheneraturebeTofdefined150asKenonetropicfindsTtempe≈31eratureK,forTe
T=200KonefindsTe≈38K,andforT=300KonefindsTe≈47K.Formolecules
withquadraticStarkshifts,suchasH2OorD2O,thenumberofcontributingstates
issectioneven4.2[smallerRie06,duetoMot09b].strongerTherefore,selectioneveninwhenthethenfilteringmoleculesprocessareasextracteddiscussedfromin
athermalreservoirthepurityoftheguidedbeamintermsofpopulatedinternal
statesisalreadyconsiderablyimproved.

Summary5.4Depletionspectroscopyconstitutesapowerfultooltoexperimentallyaccessthein-
ternalstatedistributionofguidedmolecules.Asshownforguidedformaldehyde
molecules,theexperimentallymeasuredrotational-statedistributionandtheoreti-
calpredictionsbasedonthermalsourcepopulationsandcalculationsofStarkshifts
areingoodagreement.Measurementsforvaryingsourcetemperatureshowthatby
reducingthetemperatureofthereservoir,fromwhichthemoleculesareextracted,
thepurityoftheguidedbeamcanbeimproved.Depletionspectroscopyasamethod
forinternal-statediagnosticsinacoldguidedbeamisnotrestrictedtoformaldehyde
andshouldbeapplicabletoothermolecularspeciesaswell.
Furthermore,depletionspectroscopyisnotonlyatoolforinternalstatediagnos-
tics.Forexample,itcanbeusedforspectroscopyofspecieswhicharehardtostudy
inthegasphase.Collinearspectroscopyinacoldguidedbeamhastheadvantage
oflonginteractiontimesandgoodoverlapwiththeslowmolecularbeam,makingit
agoodchoiceforstudiesofweaktransitions.Sincetheelectrostaticguideproduces
acontinuousfluxofmolecules,itisanaturalchoiceforcombinationwithnarrow-
bandcwlasers.Usingahigher-ordermultipoleguide,itshouldbepossibletoprobe
moleculartransitionsinmorehomogeneouselectricfields,resultinginnarrowlines,
andallowingforexamplemeasurementsofdipolemomentsofelectronicallyexcited
states.Moreover,byapplyingaDCelectricbiasfield,spectroscopyoforientedpolar
moleculesshouldbepossible.

6Chapter

Cavitscatteringy-enhancedRayleigh

InBoh83this]cishapter,discussed.theeffectTheofmotivanationopticalforcavitthisyonworkRaistyleighwofold:scatteringFirst[ofRaall,y99,studyingvdH81,
theinfluenceofanopticalcavityontheRayleigh-scatteringrateofsomepolarizable
whicparticlehoftenallowssometoinv“quanestigatetumness”theisclassicaascribled.natureThisoftheaspectPurcellisintereeffectst[ingPur46],mainlyto
fromaconceptualpointofview.Secondly,theexperimentconstitutesafirststep
towardsnon-destructive,in-situdetectionofcoldmoleculesbyanopticalcavity,
beinganextensionoftheefficientdetectionofsingleatomsbyanopticalcavity
[M¨un99a,M¨un99b].
Intheelectrostaticvelocity-filteringandguidingexperimentsdescribedinchap-
terpro2–duced5ofionsthiswerethesis,thenthemasscoldfilteredmoleculesandwcouneretedionizedafterbyhavingelectrboneenimpact.amplifiedTheby
asecondary-electronmultiplier.Althoughbeingaverygeneralapproach,whichis
evhasentheextendabledisadvanbytageofdepletionbeingspgenericallyectroscopytoadestructivstate-spe.Thisecificisadetectionproblemmethocommond,it
tootherexperimentsproducingcoldmoleculesaswell.Forexample,molecules
producedfromultracoldatomicensemblesutilizingaFeshbachresonancemustbe
concyclingvertedbactransitionkto[atomLan08].pairsforAlternativimagingely,thewithlasermoleculeslightcanbresonanetwithphotoionized,anatomicsuch
thatsubsequentsingle-iondetectioncanbeperformed[Dei08b].
structivCaviteydetection-enhancedtecRayleighhniques.Sincescatteringthemighlasertlightrepresenisfartandetunedalternativfromeantoythesemolecu-de-
larresonance,themoleculesbehavecompletelyclassically.Therefore,thescattering
ingprothecessadvcananbetagedescribofbedeingaslightnonsensitivscatteringetothefromspaecificclassicalmolecularoscillatingleveldipstructureole,bandear-
thereforewidelyapplicable.Sincefar-detunedlightscattering,i.e.,Rayleighscat-
tering,isweakasforinstancecomparedtoresonantscatteringinalkaliatoms,col-
lectingalargefractionofscatteredlightisessential.Thisismoststraightforwardly

83

84

Cavity-enhancedRayleighscattering

achievedusingalenswithalargenumericalaperture,therebycoveringalargesolid
angle.Analternativeandmorepowerfulapproachistocouplethescatteringobject
toanopticalresonator,eveniftherelevantlightmodeofthecavitycoversonly
asmallsolidangle.ThepotentialofferedbytheresonatorcomesfromthePur-
celleffect[Pur46],generallyassociatedwiththeenhancementofthespontaneous
emissionrateofanexcitedparticlebymeansofmirrors.Althoughspontaneous
emissionisaquantum-mechanicalphenomenon,itwasarguedthatthemodifica-
tionofitsratebytheresonatorcanbeexplainedclassicallyasalightinterference
effect[Kas62,Mil73,Dow93].ItthereforeappearsnaturalthatthePurcellenhance-
mentisauniversalphenomenon,occurringbothforlightscatteringfromquantum
objects(withdiscreteenergylevels)andclassicalobjects(oscillatingdipoles).How-
ever,whilequantum-mechanicalexperimentsonthePurcelleffectexist,theeffect
ofacavityontheclassicallight-scatteringpropertieshasbeenhardlystudied.In
arecentexperiment,asubwavelengthobjectwasplacedinthevicinityofami-
croresonator[Maz07].Here,thescatteringoffar-detunedlightintothecavitymode
wasdescribedbyasemiquantummodelfortheinteractionbetweentheclassical
oscillatingdipoleandthequantizedmodesofthelightfield.Butthisleavesopen
thequestionabouttheclassicalnatureofthePurcelleffect.Equallyimportant,a
demonstrationofthePurcelleffectforthedetectionofextremelyweaksignalsin
thisclassicalregimeisstilllacking.
TheexperimentalsetupusedtoinvestigatethecavityenhancementofRayleigh
scatteringispresentedinsection6.1.Firstdatashowingthedependenceofthe
lightscatteredfromthepolarizableparticlesonthedetuningofthecavitywithre-
specttothepumpbeamarediscussedinsection6.2.Insection6.3amodelforthe
cavityenhancementbasedontheinterferenceofclassicalscatteredelectromagnetic
fieldsisdeveloped,showingthatnoquantumeffectsareneededtoexplainanen-
hancedemissionrateinaresonator.Theactualexperimentalverificationofcavity
enhancementispresentedinsection6.4.Here,theinfluenceofthecavityonthe
powerofthelightscatteredfromthermalatomic(Xe),homonuclear(N2)orhet-
eronuclear(CF3H)moleculargasesisdiscussed.Fordifferentvaluesofthecavity
finesse,theRayleigh-scatteringrateismeasuredandcomparedtothepredictions
ofacompletelyclassicalmodelbasedontheinterferenceofintracavitylightwaves.
ThisprovesthatthePurcelleffectisclassicalandthatanexplanationintermsofa
modifiedlocalmodedensityisnotneeded.Thepowerofthelightscatteredintothe
cavityisalsocomparedtothatscatteredintothesamesolidangleinfreespace,re-
sultinginanenhancementbyafactorofupto38.Theabilitytoenhanceextremely
smalllightscatteringratesopensupnewperspectives,e.g.,forultracoldmolecules
research,whicharediscussedinsection6.5.

6.1Experimentalsetup

85

Figure6.1:Experimentalsetup.Thecavityconsistsofahigh-reflectivemirror(HR)and
anoutput-couplingmirror(OC)inavacuumchamber,whichcanbefilledwithvarious
gases.Thepolarizationdirectionofthelinearly-polarizedpumpbeamisrotatedbya
Pockelscell.Thebeamwaistisadjustedtomatchthewaistofthefundamentalcavity
modeTEM00.ScatteredlightleakingoutofthecavitythroughtheOCismodematched
intoasingle-modefiber,andthendetectedbyanavalanchephotodiode(APD).

setuptalerimenExp6.1AschematicdrawingoftheexperimentalsetupisshowninFig.6.1,whereasFig.6.2
showssomephotographsoftheactualexperimentalsetupused.Intheexperiment,
a10Wsingle-frequencylaseratawavelength−4λ=532nmwasused.Thiswavelength
wcrossaschosensectionasonathecompromiselaserwavbetwelength,eenathevλailabledeplaserendencepower,oftheandRasufficienyleightscatteringdetuning
longfromanddeep-ultrathemirrors’violetradiuselectronicofcurvtransitionsatureisof4.5thecm.usedThisspecies.comThebinationcavityresultsis0.6incma
spacingoftransversemodesof4.1GHz,largerthantheobservedDopplerwidths.
Thecavitylengthistunedbyapiezoelectrictubeseparatingthemirrors.Tomod-
ifythecavityfinesse,themirrorontheoutcouplingsideisexchanged,whileonthe
oppositesidethehigh-reflectivitymirror(HR,R=99.7%)isusedforallmeasure-
ments.Forthevariouscombinationofmirrorswithmeasuredintensityreflectivities
Rfrom=(99.7the%,cavit98.9y%,line95.9width%),asacaobservvityedfinesseinofFtransmission.=(1000,The400,ca100)vityisisplaceddeterminedin-
sideavacuumchamber,whichispumpedoutto10−2mbarbeforevariousgases
consistingofatoms(Xe),homonuclear(N2)orheteronuclearmolecules(CF3H)are
introducedviaavalve.Thefocusofthepumpbeamwasmeasuredtobe≈50µm,
comparabletothecalculatedcavity-modediameterw0≈45µm.Sincethescatter-
ingparticlesarepumpedwithapowerofupto5Wandascatteredpowerintothe
cavitymodeofafewfWisexpected,suppressionofstraylightiscrucial.Towards
thisend,lightleavingthecavityontheoutputsideiscoupledintoasingle-mode
fiber,whichisalignedforoptimaltransmissionoftheTEM00fundamentalcavity
mode.Behindthefiber,thelightisdetectedbyanavalanchephotodiodeoperated
de.motingsingle-photon-counin

86

Cavity-enhancedRayleighscattering

Figure6.2:Photographsoftheexperiment.(a)Themode-matchingsetupforthealign-
mentbeamcoupledintothecavityon-axis,andthePockelscellforpolarizationrotationof
thepumpbeamarehighlighted.Sincethelightisreflectedoffdielectricmirrorsbetween
thePockelscellandtheviewportofthevacuumchamber,correctpolarizationrotationwas
verifiedafterthepumpbeamhadpassedthroughthevacuumchamber.(b)Close-upof
thecavitywiththepumpbeampassingbetweenthetwomirrors.Ontheright-handside,
theadjustablemirrormountfortheoutcouplingmirrorcanbeseen.Apartfromeasing
thealignment,thisallowstosetthecavitylengthtothedesiredvalue,e.g.,toachievea
confocalconfiguration.Thepiezoelectrictubepermittingfinetuningofthecavitylength
islocatedleftoftheintersectionbetweenthepumpbeamandthecavityaxis.

6.2Cavitymodespectrum

87

Figure6.3:Cavityoutputmeasuredbehindthesingle-modefiber.Thesignalofthe
individualgasesisnormalizedtothesignalobtainedwithXe.Thelineprofileoriginates
fromtheDopplerbroadeningofthelightscatteredbythethermalgases.

6.2Cavitymodespectrum

Intheexperiment,thepumpbeamisalignedperpendiculartothecavityaxisas
indicatedinFig.6.1,thecavityisscannedoveratleastonefree-spectralrange,and
theintensityofthelightleakingoutofthecavityismonitored.AsshowninFig.6.3,
mainlylightscatteredintotheTEM00mode,whichisselectedbythesingle-mode
fiber,isobserved.Someresidualsignaloflightscatteredintoothercavitymodesis
presentduetoimperfectmodematchingintothefiber.Forthevariousgasesused,
thepeaksshowdifferentheightsandwidths.Thedifferentwidthsoriginatefromthe
differingmassesofthethermalgasesand,hence,thedifferingDopplerbroadenings
ofthethermalgases.Thedifferentheightsarecausedbythespecificpolarizabilities
ofthedifferingscatteringparticlesaswellasbythefrequencyoverlapsofthecavity
modewiththeDopplerprofiles.Withinexperimentalaccuracy,thebackground
signalobservedinthemeasurementswithN2andCF3Hagreeswiththeoneobtained
forXe.Dopplerbroadeningandthemultitudeofthermallypopulatedinternal
molecularstatespreventstheresolutionoftheRamanspectrum,whichcouldbenefit
fromacavityenhancementaswell[Mor07].
AsignatureofRayleighscatteringisthecharacteristicsin2θpolarizationdepen-
dencewhendrivenbylinearly-polarizedlight.UsingaPockelscell,thepolarization
directionofthepumpbeamisrotatedwithrespecttothecavityaxis.Figure6.4
showsthepolarization2dependenceoflightscatteredintotheTEM00modeofthe
cavity.Itfollowsasinθdependence,asexpectedforemissionfromaclassical
oscillatingdipole.Whenthepolarizationdirectionisalignedwiththecavityaxis
(θ=0◦),noRayleighscatteringintothecavitymodeisexpectedduetothesmall
solidangleofthecavitycoveringonlythenodallineofthedipolepattern.The
residualsignalamplitudeof1–2%canbeexplainedbyimperfectlinearpolarization

88

Cavity-enhancedRayleighscattering

Figure6.4:PolarizationdependenceoftheRayleigh-scatteredlightfromanyofthethree
gasesused.Whenthepolarizationdirectionofthepumpbeamisalignedwiththecavity
axis,noscatteringintothecavityoccurs.Intheoppositecase,polarizationdirection
perpendiculartothecavityaxi2s,themaximalamountoflightisscatteredintothecavity.
Thesolidcurveisafitofasinθpolarizationdependencetothedata.Forlightscattering
fromaclassicaloscillatingdipole,suchasin2θpolarizationdependenceisexpected.

ofthepumpbeam.Thissin2θdependenceobservedforallgasesisthecharacteristic
featureforascatteringprocessinvolvinganoscillatingdipole.
AsshowninFig.6.5,thelineshapeisdeterminedbyDopplerbroadening√for
lowdensities.Duetothe90◦scatteringgeometry,aDopplerwidthαobs=2αDis
observed,withαDbeingthestandardDopplerwidthofabsorptionspectroscopy.By
varyingthepressure,alineardependenceofthescatteredpoweronthegasdensity
isoberved,therebyrulingoutscatteringoffsurfacesasthesignalsource.Also,the
expectedlineardependenceoftheRayleighscatteredlightonthepumpbeampower
overtheentireexaminedrangeof0.1–5Wisfound.However,whenincreasingthe
gaspressurefrom100mbar,wheretheexperimentistypicallyoperated,tovalues
ofupto1bar,theappearanceofsubstructureontheDoppler-broadenedpeaksis
observed.ThesesidebandsarecausedbyBrillouinscatteringondensitywavesin
thegas[GM80,Pan02].

6.3Classicalwave-interferencemodelofcavityenhancement

89

Figureobtained6.5:forthedifferenDoppler-broadenedtpressureslinehaveprofilesbeenforCFindividually3H.Thenormalizeddataoftothethecavitymaximalscans
isvalue.shownIninthered.Atmeasuremenhighertwithpressure,lowestsidebandspressure,thecausedbytheoreticallyBrillouinpredictedscatteringDopplerappear.profile

6.3Classicalwave-interferencemodelofcavity
tenhancemen

Tomodeltheexperiment,thescatteringfromapolarizableparticle,aclassical
oscillatingdipole,intoasinglecavitymodeisconsidered.AsindicatedinFig.6.6,
theparticleispumpedfromthesidebytheelectricfieldEp.Theelectricfield
scatteredbytheparticleintothecavitymodetravelinginonedirectionisexpressed
asEsc=αEp,withαbeingaproportionalityfactor(whichequals,exceptfor
numericalprefactors,thepolarizability).Toderiveanexpressionfortheintracavity
fieldandfinallythepowerscatteredintothecavitymode,allpossiblecontributions
totheintracavitylightfieldaretakenintoaccount.Thesecontributionsmodifying
theintracavitylightfieldononeroundtriparelightscatteringfromthepumpbeam
intothecavitymodeandlossesbytransmissionoftheintracavityfieldthroughthe
mirrors.

6.3.1Theintracavityfield

Fig.The6.6.differenThetconscatterertributionsemitstoantheintracaelectromagneticvitylighfieldtfieldintoaarerighschtandematicallyaleft-trashovwnelingin

90

Cavity-enhancedRayleighscattering

Figure6.6:Theorysketch.Differentcontributionstotheright-travelingintracavityfield
atFieldthepscatteredositiontoofthetheleft,scatteringafteroneparticle.reflection(a)atFieldthemirror.scattered(c)intoIntrtheacarvitighytfielddirection.afterone(b)
trip.round

wave,whichcaninterfere.Theright-runningintracavityfieldEcatthepositionof
thescattererisfoundbyaddingupallcontributions,leadingto
Ec=αEp+r1eik(d+2Δz)αEp+r1r2e2ikdEc,(6.1)
whereriarethemirror’samplitudereflectioncoefficients(ri2=Riisthemirror
reflectivity).Thecavitylengthisdenotedbyd,2ikandΔzk=2π/λisthewavenumber
ofthelightfield.TheadditionalphasefactoreaccountsforatranslationΔz
ofthescattereralongthecavityaxis.BysolvingEq.(6.1)self-consistently,thefield
scatteredintothecavityisfoundtobegivenby
1+r1eikde2ikΔz
Ec=αEp1−r1r2e2ikd.(6.2)
Inthefollowing,aresonantcavityisassumed,e2ikd=1.Tocalculatetheintensity
runningintherightdirection
Ic=c20|EcEc∗|(6.3)
forarandomly-distributedgas,anaverageoverthepositionoftheparticles,i.e.,
−λ/2≤Δz≤λ/2,mustbetaken,resultingin
21+r12
Ic=αIp(1−r1r2)2.(6.4)
Forhighmirrorreflectivities,Ri=ri2≈1(i=1,2),thiscanbeapproximatedby
Ic≈2α2Ip(F/π)2(6.5)
√√√withthecavityfinesseF=π4R1R2/(1−R1R2)≈π/(1−R1R2).Inanintuitive
picture,F/πisthenumberofreflectionsinthe2resonator.Theelectricfieldincreases
linearlywiththisnumber,henceIc∝(F/π).

6.3Classicalwave-interferencemodelofcavityenhancement

91

Forthefollowingdiscussion,itisconvenienttoconvertallintensitiesIintopowers
Pusingtheareaofthecavitymodeasareference.FromEq.(6.5),thepowerleaving
thecavitythroughtherightmirrorisfoundtobegivenby
Pt=T2×Pc≈4T2/(T1+T2)α2PpF/π,(6.6)
√√whenr=R=1−TandtheTaylor-seriesexpansion
F≈√1=1
π1−R1R21−(1−T1)(1−T2)
(6.7)21=≈1−1−(T1+T2)+T1T2T1+T2
areinserted.Forthesymmetric-cavitycase(T1=T2=T),thissimplifiesto
Pt≈2α2PpF/π.(6.8)
Therefore,theenhancementofthedetectablescatteredpowerintooneoutputmode,
i.e.,leavingthecavitythroughoneofthemirrors,comparedtothesituationwithout
thecavity,isgivenby2F/π.Sincehalfofthelightleaksoutoftheleftcavitymirror,
thetotalpowerscatteredintothecavitymodeisgivenby
Pcav=2Pt≈4α2PpF/π.(6.9)
Forparticlesmaximallycoupledtothecavity,i.e.,noaveragingoverparticleposi-
tion,anadditionalfactor2comesin
Pcav=8α2PpF/π.(6.10)
Thishastobecomparedtothetotalpowerscatteredintofreespaceintothemode
definedbythecavitybutwithoutthecavityenhancement,whichis
PfsΩcav=2α2Pp.(6.11)
Therefore,thecavityenhancesthepowerscatteredintothesamemodeoftheelec-
tromagneticfieldbyafactor4F/πascomparedtothefree-spacesituation.
6.3.2Comparisontofree-spacescattering:ThePurcell
factorSofar,onlyasinglemodeoftheelectromagneticfieldwasconsidered.Thereby,
thepowerscatteredintothecavitymodewascomparedtothepowerscatteredinto
thesamemodeinthefree-spacesituation.Suchascenarioisoftenfacedinthe
experiment,whereoneisonlyinterestedinthelightscatteredintoasinglemode
whichcan,e.g.,beefficientlycoupledintoasingle-modeopticalfiberfordetection.
Itis,however,alsointerestingtocomparethepowerPcavscatteredintothecavity
tothepowerPfsscatteredintothefull4πsolidangle.

92

Cavity-enhancedRayleighscattering

Figure6.7:(a)Beamwidthw(z)ofthelowest-ordertransverseHermite-Gaussian2cavity
mothedeRaTEMyleigh00alonglength.its(b)propagatEmissionionpatterdirectionnofzthe.w0isclassicalthebeamoscillatingwaist,dipandolez0orien=πtedw0alon/λgis
-axis.zthe

Overlapbetweendipoleemissionpatternandcavitymode
Forthis,theoverlapintegralbetweentheintensity-normalizedelectricfieldsof
thedipoledipoleemissionmodepatternandthearecascvityhematicallymodeareshoevwninaluated.Fig.6.7The.Thecavityscalarmodipdeoleandmothede
Edip(θ,r)canbedefinedininsphericalcoordinatesas
13Edip(θ,r)=8πrsin(θ),(6.12)
wherethephasevariationexp(ikr)alongthepropagationdirectionrhasbeenomit-
ted.Thedipolemodeisnormalizedtoitsintensity,
Edip(θ,r)2r2sin(θ)dθdϕ=1.(6.13)
Intheexperiment,thelowest-ordertransverseHermite-GaussianmodeTEM00
wcoasused.ordinatesTheisgivelectricenbyfieldofthefundamentalcavitymodeEcav(r,z)incylindrical

2r1Ecav(r,z)=N(z)exp−w(z)2,(6.14)
vcawherethephasevariationalongthepropagationdirectionzhasbeenomitted.
Ncav(z)isanormalizationconstant(seeEq.(6.17)),andw(z)isthebeamwaist
2λzdefinedas2
w(z)=w01+z=w01+π2w4z2.(6.15)
00Themodeisnormalizedintoonedirectionas
Ecav(r,z)2rdrdϕ=1,(6.16)


(6.16)

6.3Classicalwave-interferencemodelofcavityenhancement

93

requireshwhic22Ncav(z)=πw0+λ2z2.(6.17)
wπ220Now,theoverlapintegralbetweentheintensity-normalizedelectricfieldsofthe
dipolemodeEdip,Eq.(6.12),andthefundamentalHermite-Gaussiancavitymode
Ecav,Eq.(6.14),areevaluatedinthefarfieldatafixedvaluez.There,thedipole
modeandthecavitymodehavephasefrontslyingonspherescenteredattheposition
ofthescatterer.Theoverlapinonepropagationdirectionzisgivenby
η=E∗dipEcavΩ.(6.18)
ADuetothesmalltransverseextentofthecavitymode,thedipolemodeEdipis
approximatedbyitsvalueonthez-axis,
13Edip(θ=π/2,z)=8πz.(6.19)
inresultsThis31√3w0√3λ
η=Ecav8πzrdrdφ=2z+2πw0,(6.20)
whichinthelimitz→∞convergesto
√λ3η=2πw0.(6.21)
Thefractionofthefull4πsolidanglecoveredbythecavitymodeΩcavisgivenby
theratiobetweenthepowerscatteredintothecavitymodeandthetotalpower
scatteredintothedipolemode.Hence,
2λ3Ωcav=2η2=2π2w2,(6.22)
0wherethefactor2comesintoplaysinceintheevaluationoftheoverlapintegral
onlyonedirectionofthecavitymodewastakenintoaccount.Here,theintensities
aresummedupandnotthefields,sincethereisnointerferencebetweenthefields
scatteredintothetwodirections.

(6.20)

scatteringfree-spacetoComparisonThepowerscatteredintothemodedefinedbythecavityinthefree-spacesituation,
i.e.,withoutthecavityenhancement,is(seesection6.3.1)
PfsΩcav=2α2Pp.(6.23)

94Cavity-enhancedRayleighscattering
Usingtheeffectivesolidangleofthecavitymode,thetotalpowerscatteredintofree
spaceisgivenby22
Pfs=Ω1cav×PfsΩcav=43πλ2w0α2Pp.(6.24)
particleTherefore,themaximallyratiobcoupledetweentothethepcaowviteyrPandcavthescatteredtotalpoinwtoerPthefscavitscatteredymoindetobyfreea
spaceisfoundtobe
Pcav8α2PpF/πλ2
Pfs=4π22w02α2Pp=6π2w02F/π.(6.25)
λ3factorPurcellThespInontheliterature,taneous-emissionprocessesrates[moGody83ified,byHei87the]aretpresenceypicallyofacavitconnectedysuchtoastheenhancePurcelld
factor[Pur46].ThePurcellfactorisdefinedas
Q332C=4π2λV,(6.26)
withQthequalityfactorofthecavityandVthemodevolume.Foranatomic
system,thefree-spaceatomic-polarizationdecayrateγischangedtothevalue
γsition=(1+frequency2C)γ.bFyortheatwopresencemirrorofFacaabry-Pvityerotbeingcavity,resonanthetmowithdevtheolumeatomicViswtran-ell
ybximatedapproV=πw02L/4.(6.27)
TheandδQνthefactorcaisvitydefinedlinewidth.asQ=Forν/δaνFwithabry-Pνerotthecavitresonancey,thiscanfrequencybeofrelatedthetocavitthey
cavityfinesseFandthecavitylengthLvia
1cF=2Lδν(6.28)
andc/λνQ=δν=δν.(6.29)
Therefore,thecavityQfactorcanbeexpressedintermsofthecavityfinesseFand
cavitylengthLas
Q=2λLF.(6.30)
Puttingalloftheabovetogether,onefindsforthePurcellfactorofastanding-wave
Fabry-Perotcavity
3Q3(2L/λ)Fλ2
2C=4π2λ3V=4π2λ3πw2L/4=6π2w2F/π.(6.31)
00

6.4Cavity-finessedependenceofRayleighscattering

95

Figure6.8:SpectralOverlapbetweentheDoppler-broadenedscatteringprofileandthe
Lorentziancavitylineshape.(a)Doppler√profileforthedifferentroom-temperaturegases
usedintheexperiment.Thefactor2duetothe90◦scatteringgeometryisincluded.
(b)Calculatedspectralprofileofthecavityresonanceforthedifferentvaluesofthefinesse
employedintheexperiment.ThedashedcurvesarethesameDopplerprofilesasshown
in(a),whichvaryonlyslightlyoverthefrequencyrangespannedbythecavitylinewidth.

inThisisterferenceexactlymodel,theEq.same(6.25).expressionTasherefore,theonetheobtainedclassicalwausingve-intheterferenceclassicalwmoavdele-
ofpresenscatteredtedherefieldssho[wsKas62that,theMil73,PurcellDow93factor].isindeedfullyexplainedbyinterference

6.4Cavity-finessedependenceofRayleigh
scatteringInsection6.2,thespectralprofilesofthelightscatteredintothecavityweredis-
cussed.There,themodestructureofthecavitywasclearlyvisiblefromthedistinct
transversecavitymodesinFig.6.3.However,thismeasurementdidnotyetallowa
conclusionwhetherthecavityindeedenhancestheamountofscatteredlight.There-
fore,measurementswereperformedfordifferentvaluesofthecavityfinesse,under
conditions.ticalidenotherwise

6.4.1Influenceofthecavityfinesseonthespectralprofiles
ofBeforethethermalcomparingmotiontheisexpbrieflyerimentaldiscussed.resultstoThethefrequencytheoreticaldependencepredictions,ofthethepoweffecter
scatteredfromapolarizablemediumintothecavityisgivenbytheconvolutionof
thecomparesLorenthetziancaDopplervitylineprofilesshaofpethewithvariousthethermalDoppler-broadenedgaseswiththeprofile.spectralFigureprofile6.8s
ofDopplerthecavithalf-wyforidthsdiffereαDntarevalues0.50ofGHztheforcaCFvit3yH,finesse.0.78GHzForfortheN2ga,seandsused,0.36GHzthe1for/e

96

Cavity-enhancedRayleighscattering

Figure6.9:Dependenceofscatteredpoweronthecavityfinesse,measuredwithXe
at0.1bar.Thedataiscorrectedforthelimitedoverlapofthecavitymodewiththe
Doppler-broadenedspectrumoftheRayleigh-scatteredlight.

√Xe.Hence,theexperimentallyrelevantDopplerhalf-widthαobs=2αDismuch
largerthanthecavityHWHM(HalfWidthatHalfMaximum)κ,whichtakesa
valueof≈125MHzforthelowest-finesseresonator.Forathermalgas,increasing
thecavityfinessedoesnotincreasetheoverallpowerofRayleighscatteredlightinto
thecavitymode.Althoughthepowerscatteredbyamoleculebeingresonantwith
thecavityincreaseslinearlywithcavityfinesse,thenumberofresonantmolecules
decreaseslinearlywithκ(forκαobs).Hence,thesetwoeffectscancel.Onlyfor
coldscatterers,whentheDopplerwidthbecomessmallerthanthecavitylinewidth,
increasingthecavityfinessepaysoffintermsofobservablesignal.

6.4.2Cavity-finessedependenceofthescatteredpower
Tcaovittestytheoutputexppowectederwdepasendencemeasuredofforthethescatteredthreeapvowerailableonvthealuescaofvitythecaparameters,vityfinessethe
F=(1000,400,100).ThespectraloverlapsofaDoppler-broadenedthermalXegas
thewiththemeasuredcavitymosignalsdes(52are,85,(4.2,90)10.1,fW,33.4)the%forscatteredtheporespwerectivfromelyusedparticlescaatvities.restFwromas
calculatedtoeliminatetheeffectofthermalmotion,i.e.,theDopplerbroadening.
inTheterferenceresultformoXedelisandshothewninPurcellFig.factor,6.3(d).alinearAsdeppredictedendencbeyonthethecaclassicalvityfiwanesseve-
Fisromfound.theexpTheerimenscatteredtarapotiowerbetalsoweendependsscatteredonptheowpersforolarizabilitXe,yCFof3H,theandNparticles.2of
(1:0.35:0.1)isdeterminedforfixedcavityfinesse.Basedontheirpolarizabilities
[isinLid90go,odMil81]agreemenandtDopplerwiththeobservbroadenings,ations.ratiosTheofgo(1:od0.36:agreemen0.09)tareagainexpected,confirmswhictheh
validityoftheclassicaloscillating-dipolelight-scatteringmodel.

Summary6.5

97

totheFinally,free-spacethesituenhancemenationtisofshothewn.Fscatteredorthispomwerleaeasuremenvingt,thethecavitysingle-moasdecomparedfiber
wasusedtoselectthesamemodeinthefree-spacescatteringexperiment.Under
theotherwisecavityidinenplacetical,aconditionsscattered(100pomwerbarofXe≈1.3pressure,fWis1Wobservpumped.poAwer),factorbutoftwwithoutois
estimatedfortheaccuracyofthismeasurement,constrainedbymode-matching.
≈This50pfWowermeasuredmeasuredwithinacafree-spacevityfinessescatteringof1000,hastoanbeenhancemencomparedttoofthe38.vToaluetestof
thebroadenedclassicalspmoectraldelforprofilethecawithvitythecavitenhancemenymot,detheof4.2limited%,owhicvherlapdoofesthenotoccurDoppler-in
arethetakenfree-spaceintoaccounscattering,t.andPuttingthetheseenhancemtogethener,tbayvthealuecaofvit≈y2.with0fWaisfinesseexpofected1000for
thefree-spacescatteringmeasurementwithoutthecavity,taking≈50fWmeasured
andwithmethecaasuredvityasenhancemenreference.tsareWithinintheagreemenexpt,erimenshowingtaltheuncertainprocessties,iswtheelldescribcalculateded
bytheclassicalmodel.

Summary6.5InthischapterithasbeenshownthattherateofRayleighscatteringcanbeen-
hancedbyplacingathermalgasinanopticalcavity,similartothePurcelleffect
generallyassociatedwithenhanced(orinhibited)spontaneousemission.Compared
tothefree-spacesituation,theenhancementfactorforscatteringintothefundamen-
talcavitymodeisfoundtobeashighas38.Theresultsareingoodagreementwith
themodelofaclassicaloscillatingdipolecoupledtothecavitymode,showingthat
theoriginsofthePurcelleffectarebynomeansquantum-mechanicalbutinstead
explainablebyaninterferenceeffectofclassicalwaves.
Theexperimentshowsthepotentialofanopticalcavitytoincreaseweaksig-
nalsinlight-scatteringexperiments,whichshould,inprinciple,beextendableto
Raman-typescattering[Mor07].Thelargedetuningofthelaserlightfromany
opticaltransitionallowsthemethodtobeappliedtodifferentspeciesasdemon-
stratedwiththeuseofXe,N2,andCF3H,independentoftheirspecificinter-
nallevelstructure.Thisopensanewpathwaytoopticaldetectionofdeeply-
boundultracoldmolecules,forwhichtheefficientproductionwasreportedrecently
[Sag05,Osp08,Dan08,Dei08b,Lan08,Ni08,Vit08,Ni09,Osp09].Sofar,however,
detectionofthesemoleculesrequireseitherdissociationtounboundatompairsor
ionization.Here,cavity-enhancedRayleighscatteringmightbeanattractivein-
situdetectiontechniquesinceitdoesnotrelyonclosedcyclingtransitions.Al-
thoughinthedescribedexperimentroom-temperaturegasesattypicaldensitiesof
2.5×1018cm−3wereused,thenumberofparticlescontributingtothescattering
intothecavityisonly≈1010foracavityfinesseof1000.Theaforementioned
moleculeproductiontechniquescantypicallyprepare105ultracoldmoleculesat

98

Cavity-enhancedRayleighscattering

cloudsizescompatiblewiththecavity-modediameterinthepresentedexperiment.
SinceDopplerbroadeningisabsentforlightscatteredbythesetrappedultracoldmo-5
Flecules,urthermore,thecavitalkyalifinessedimerscanhabveeamoreincreasedthanto10an×explargererimenptallyolarizabilitrealisticyαvasalueofcompared10.
αto,Xewhichusedasshouldagivrefereneacelowgaserinboundthefordescribtheedpomeasuremenlarizabilitiestsat(staticopticalpolarizabilitiesfrequencies:
KRb:502a.u.,Cs2:670a.u.,Xe:27.3a.u.,1a.u.=0.148A˚3)[Lid90,Dei08a],andthe
2Rateringratesyleigh-scatteringintothecacrossvityonsectiontheσorderscalesofas10σ0∝kHzα.canAllbeantogether,ticipatedensemforblesuchscat-an
tonsultracoldatamtotalolecularrateonsample.theorderItoffollo1wsHz,thatwhereonatheverageratioevbeteryweenmoleculescatteringscattersintopho-the
cafore,vitycaandvity-enhancedscatteringinRatoyleighfreespacescatteringPcav/Pfsmigh≈t2alloforwtheforgivaennearlyparameters.demolition-freeThere-
setup,detectionthewitusehofalmostdegeneratenopcavitieshoton-recoilcouldboheating.osttheAspoanwerextensionscatteredofinthetothepresencavittedy
withthenumberofincorporatedmodes[Cha03].Collectiveenhancementeffects
[Dom02],observedforatomicensembles[Bla03],couldfinallyresultinanadditional
signal.ofincrease

7Chapter

okOutlo

Inthelastyears,theelectrostaticvelocity-filteringandguidingtechniquehasbeen
bdeveamselopofedincoldthepolarRempemoleculesgroup.isAitskeyfeatureapplicabilitofythistomethodifferendttomoprolecularducespcontinecies.uousIt
demandsonlyforafavorableratioofStarkshifttomassandthepresenceoflow-
field-seekingstatespopulatedinthesourcefromwhichthemoleculesareextracted.
Thefluxofmoleculesissohigh(upto1011s−1atdensitiesof109cm−3andtypical
velocitiesof50m/s[Ran03,Jun04b,Som09,vB09]),thattheyareeasilydetectedby
aofquadrupcollisionsoleinthemassspvicinityectrometer.oftheThenozzleacforhievableincreasingfluxisreservfinallyoirlimitedpressure.byEsptheeciallyonset
theeffectsslowbestecomemoleculesobservareableevtherebenyinexptheelledfromnear-effusivtheebregeam,imesucinhthatwhichthesethesourcecollisionalis
].Mot09a[eratedopThetributionofselectivitymoleculesoftheinguidedifferenontintheternalmolecularstatestoStarktheshiftguidedisbeaevidenm.tDepfromendingthecon-on
itsrotationalstateamoleculeexhibitsauniqueStarkshift.Therefore,rotational
forstatesmolecularwithlargespeciesStarkwithshiftsconsystematicallytributedistronglyfferingtotheStark-shiftguidedbehabvioream.Condifferenvterselyeffi-,
cienciesforelectrostaticvelocityfilteringareobserved.Takingthewaterisotopologs
asanexample,afluxofguidedmoleculesisachievedforHDOwhichislargerby
formorethisbthanehavioorderrofarestatesmagnitudewithasmainlycomparedlineartoStarkthatofshiftsH2inOandHDOD2andO.theRespquadraticonsible
ofStarkguidedshiftsofmoleculesH2OonandDthe2O.appliedAsaelectroconsequence,devaoltagespisecificobservdepedendenascewellof[theMot09bsignal].
Theinternal-statedistributionofguidedmoleculesisevenmoredirectlyaccessible
bydepletionspectroscopy.Usingultravioletlaserexcitation,guidedformaldehyde
moleculesareopticallypumpedtoapredissociatingelectronicstate.Thelaser-
frequency-dependentmoleculelossrevealsthecontributionofindividualrotational
Starkstatestoshifttheanditsguidedpbeam.opulationinThesetheconthermaltributionssourcedepasendondescribtheedbymolecularthemodelstates’of
velocityfiltering[Mot07].

99

100

okOutlo

Allmeasurementspresentedinthisthesisshareonefeature:Theguidedmolecules
aredetectedbyaquadrupolemassspectrometer.Thisisadestructivedetection
process,whichiscommontomostothermethodsinthefieldofcoldmolecules.
Forexample,moleculeswhichareproducedusingmagneticFeshbachresonances
aredissociatedtoatompairsbeforebeingimagedwithresonantlaserlight.For
manyapplicationsitisdesirabletohaveanon-destructivedetectionmethodat
hand.Cavity-enhancedRayleighscattering,whichhasbeenobservedforroom-
temperaturegases,mightpermitsuchin-situ,non-destructivedetectionfordense
samplesoftrappedultracoldmolecules[Mot09c].
Inthefollowingsections,somepossibleapplicationsandfutureextensionsofelec-
trostaticvelocityfilteringandguidingarediscussed.Theextensionofdepletion
spectroscopybeyondinternal-statediagnosticsandthestudyofcoldcollisionsare
presentedinsection7.1aspossibleapplicationsoftheguidingtechnique.Ongoing
developmentsintheRempegrouparediscussedinsection7.2.Ontheonehand
side,theyadvertisetheuseofelectricguidesasaverygeneralsourceforcoldbeams
ofpolarmolecules.Meanwhile,thetechniqueisbeingcopiedandbeingusedina
numberoflaboratoriesaroundtheworld(guidingwithelectrostaticfields:[Bic05,
Tsu07,Hel08,Hum08a,Pie08,Wil08a,Wil08b,Bel09a,Mom09,Mud09,Pat09],
guidingwithalternatingelectricfields:[Fil08,K¨up09,Wal09]).Ontheotherhand
side,theyshowthenecessityforthedetailedunderstandingofthevelocity-filtering
processwhichwasgainedinthisthesis.Especiallyindividualinternalmolecular
statesbecomeevenmoreimportantforthenewcoolingandtrappingschemesunder
development.Thispointsoutthesignificanceoftheacquiredproficiencyabouttheir
influenceonvelocityfilteringandguiding.

7.1velocitExtensionsyfilteringandandapplicationsguidingofelectrostatic

7.1.1Spectroscopyofcoldmolecules
Sofar,depletionspectroscopyhasbeenperformedwithguidedformaldehydemo-
leculesinthenear-ultravioletspectralrangeforinternal-statediagnostics.The
amoleculesdecreaseareintheopticallyfluxofpumpguidededtoanmoleculesexcitedpropstateortionalwhichtothepredissopciates,opulationsuchofththate
addressedinternalstateisobserved.Pumpingtoadissociatingstateis,however,
nottransferathenecessarymoleculesconditiontosomeforinternalapplicationstateofthiswhichismethonotd.guidedInstead,anymitisore.sufficienThistmatoy
beeitherahigh-field-seekingstateoralow-field-seekingstatewithasignificantly
nal,smallerdepStarkendentshiftonasthepcomparedopulationtoofthetheinitialaddressedstate.inInternathislsituationmolecularastate,depletionwillsbige-
observableaswell.Therefore,thedepletion-spectroscopytechniquecouldbetrans-
ferredtootherfrequencyrangestoaddressdifferentspecies.Manymoleculeswhich

7.1Extensionsandapplicationsofelectrostaticvelocityfilteringandguiding101

hationsvebineenthesuccessfullymid-infraredvelocitrangeyfilteredaroundand3–5µmguided[[Zep09Som09].In]hathisvewavvibrationalelengthtransi-range,
opticalparametricaloscillators(OPOs)areavailableastunablenarrow-linewidth
conFtinuurthermore,ous-wave(cw)depletionorsppulsedectroscoplasers.yisnotonlyatoolforinternal-statediag-
thenostics.purityItofcanthebeguideuseddasbweam.elltoSpdepectroscopopulateyinunawancoldtedandstates,guidedtherebbyeamofincreasingpolar
themoleculesstudyofoffersweaktheadvtransitions.antageInofthelonginpresenteractedtionexptimes,erimentthemakingobservitattedractivlineshapefore
andguidinglinewidthelectricofthefield.Totransitionscircumwvasentcausedthis,bspytheectroscopmagnityudecouldofbtheepinherformedomogeneouswith
moleculesoccupyingatrapvolume,inwhichhomogeneouselectricfieldsarapplied.
inThisteractionwouldtimesresultinwithsmallerthelaserlinewidtlight.hsandSuchasaantrapcanadditionalbebenimplemefitenintedevenwithlongermi-
crostructuredelectrodearraysinawaycompatiblewiththeelectrostaticguiding
].Zep09[system

7.1.2Collisionexperimentswithcoldmolecules
Duetotheirhighfluxandcontinuouscharacter,coldguidedbeamsproducedby
electrostaticvelocityfilteringpromisetobeanexcellentstartingpointfortheinvesti-
gationofcoldcollisionsandcoldchemistry.Theapplicabilityoftheelectricguideas
acoldmoleculesourceforsuchcollisionstudieshasalreadybeendemonstratedinan
experimenttargetinglaser-cooledtrappedatomicCa+ionswithcoldguidedCH3F
molecules[Wil08a,Wil08b,Bel09a].Conceivableexperimentsincludecollisionsbe-
tweenthecoldguidedbeamandultracoldatomsinamagnetoopticaltrap(MOT),
whichmightevenbeextendabletosympatheticcoolingofpolarmolecules.Inare-
centpaper,P.S.˙ZuchowskiandJ.M.Hutsonpresentedcalculationsofcrosssections
forlow-energeticcollisionsofNH3andND3withultracoldRbatoms[˙Zuc09].These
calculationsfocusonNH3(ND3)moleculesintheuppercomponentoftheinversion
doubletofthe|J=1,K=1state(11u).Thislow-field-seekingstateisusedfor
Starkdecelerationandalsopreferentiallypopulatedincoldguidedbeamsproduced
byelectrostaticvelocityfilteringincombinationwithbuffer-gascooling.According
totheirresults,thecross˚2sectionforelasticcollisionsbetween−NH13orND3andRb
isontheorderof1000Aoverawideenergyrange(1–100cm),whilethecross
sectionforinelasticcollisionsispredictedtobeontheorderof100A˚2.Forlower
collisionenergies(butnottoosmall,≥100µK)theelasticcrosssectionforND3-Rb
collisionsisstilllargerthantheinelasticcrosssectionfortransitionstothehigh-
field-seekinglowercomponentoftheinversiondoubletofthe|J=1,K=1state
(11l),however,notbymorethanafactoroften.Thisrathersmallratiomakesthe
realizationofsympatheticcoolingtoultracoldtemperaturesthroughthecombina-
tionofelectrostaticallytrappedND3moleculesinalow-field-seekingstatewithRb
atomsnottoofavorable.Asapossiblewayout,P.S.˙ZuchowskiandJ.M.Hutson

102

okOutlo

couldsuggestshothatwmNDuch3moremoleculesfavinorableacollisionhigh-field-seekingpropertiesstatewithtrappedbmagneticallyyACelectrapptricedfieldsRb
atoms,whichmightpermitsympatheticcooling.
CombiningthecalculatedcrosssectionforND-Rbcollisionsofσ=10−13cm2
[˙Zuc09]withthefluxofΦ=1011molecules/sproduced3bytheelectricguide[Som09,
vB09],someestimatescanbemadeforanimaginablecollisionexperimentbetween
tralthetwoatomssp[ecies.Met99W].eToassumeensureagocloudodofovlerlapaser-cobetoledweenatomstheisatomsheldinandathetrapformolecularneu-
beam,moleculesthearetrapphotedatomcomparedcloudtocanthebepdepthositionedoftheinsidetraptheholdingelectrictheguide.atoms,anSinceatomthe
undergoingacollisionwillbeexpelledfromthistrap.Theexperimentallyacces-
thesiblescatteringsignaturerateforandcollisionsNtheistheatomnrelativumbeer.lossIfratetheofsizeofatomsthe,R/atomN,withcloudRisbsmalleing
comparedtothediameterofthemolecularbeam,thisrelativeatomlossratecan
beestimatedbyσ
R/N=Φ×d2m,(7.1)
withdmbeingthediameterofthemolecularbeam.Thisformulaismotivatedas
follows:psc=σ/d2mistheprobabilityforasinglemoleculeintheguidedbeamto
ofundergothetrapabycollisionacollisionwithawithsingleanyatom.oftheTheguidedrate,withmolecules,whichanisatomthereforeiskicgivkedenoubyt
bΦ×eampscof.dPutting≈0.1incmthenresultsumbinersagivenrelativabeovelossratetogetherofwithatomstheofsizeR/Nof≈the1smo−1.lecularThis
mshouldbeobservableinanexperiment,consideringtypicallifetimesontheorderof
10sfortrappedneutralatoms.Asanalternative,onecouldplacetheatomcloud
behindtheexitoftheguidetoavoidinfluencesoftheelectricguidingfields.Note
thatthedensityofmoleculeswouldbereducedinsuchanexperiment,sincethe
Nevmolecularertheless,beamthefluxspreadsofoutmoleculeswhenleavingthroughthetheguidingatomcloudstructureshould[Jun0still4b,beSom09high].
enoughtocauseameasurablelossofatoms.

7.2OngoingdevelopmentsintheRempegroup
Inthissectionongoingdevelopmentsinthecoldmoleculesgrouparepresented.
Thecombinationofelectrostaticvelocityfilteringwithbuffer-gascooling,which
allowstoproducehigh-fluxbeamsofinternally-coldpolarmolecules,isdiscussed
insection7.2.1.Theavailabilityofsuchahigh-puritybeamofmoleculesallows,
e.g.,theinvestigationofinternal-state-dependentcrosssectionsincoldcollision
experiments.Tobridgethegapfromthecoldtotheultracoldregime,acooling
schemebasedoninfraredtransitionsinsuitablytailoredtrappingelectricfields
isunderdevelopment.Themainideasofthisopto-electricalcoolingschemeare
presentedinsection7.2.2.

7.2OngoingdevelopmentsintheRempegroup

103

andFigureelectrostatic7.1:Schematicextraction.represenMoleculestationofaretheinjectedsetupincomtobtheiningcoldcrybufferogenicgasbuffer-gasthroughacowolingarm
inputcapillary.Inthebuffer-gascelltheirtranslationalandinternaldegreesoffreedom
arethroughcooledthebyexitcollisionsholeandwithwhictheharecoldinaheliumloatoms.w-field-seekingSlowinternalmolecules,statewhic,hareleavcollecethetedcellby
theelectrostaticguide.Thesemoleculesarethentransportedoutofthecoldenvironment,
wheretheyaredetectedbytheQMS.

7.2.1Electrostaticextractionofmoleculesfromacryogenic
sourcebuffer-gas

Insection5.3itwasshownthattheinternal-statedistributionofguidedformalde-
hydemaximallymoleculesachievisablepurifiedtempbyeraturereducingreductionthewithsourcethetempliquid-erature.nitrogen-coNonetheless,olednozzlethe
suredescribofedtheinformaldehsection2.2ydeisgaslimitedintheto150nozzleK.bBeloecomeswlothiswertempthanerature,thettheypicalvapoporerationpres-
pressure.Thiscausescondensationofthemoleculesonthewallsoftheeffusive
sourceandastrongreductioninthefluxofmolecules.Tocircumventthisproblem
thewithamoleculescoldbuffermustgas,becothereboledybayvothoidingermeans.collisionsThiswithcanabcoldeacwallhiev[Wedei98by].Incollisionsuchs
experimentsheliumistypicallyusedasabuffergas,sinceitistheonlygastohave
asufficientlyhighvaporpressureattemperaturesofafewKelvin.
Inthelastfewyearsasetupcombiningcryogenicbuffer-gascoolingandelectro-
staticvelocityfilteringhasbeendevelopedintheRempegroup,therebymerging
shothewnadvinanFig.tages7.1of.theWtwarmoapproacmoleculeshes[areSom09injecte,dvB09in].toaThecryprinogenicciple(Tis≥sc4hK)ematicallyhelium
buffergas.Boththetranslationalandinternaldegreesoffreedomofthemolecules
thearecocelloledthroughbyacollisionssmallexitwithholethecoandldwhicheliumhareinatoms.aloSloww-field-seekingmolecules,inwhicternalhleastate,ve

104

okOutlo

Figure7.2:Temperaturedependenceofthedepletionsignalforguidedformaldehyde
(H2CO)molecules.Thislaser-induceddepletioninthesignalofguidedmoleculesispro-
ptheportionalopultoationtheinptheopulationlowintheer-energeticaddressedrotationalrotationalstatesstate.increasesForloandwerthecellpurittempyerofaturesthe
|1,guided1,0bconeamistributesimpro2%ved.toFtheorcomguidedpbarison,eam.ataThisvsourcealuetempincreaseseraturetoof4%300atKathetempstateer-
atureof150K,thelowestoperabletemperatureusingtheliquid-nitrogen-cooledsource
tecdescribhnique,edinthechaptconer2.tributionBycoofolingthisthestateisreservenoirhancedto4Ktoand80%[utilizingSom09,thevB09]buffer-gas-cooling

arecollectedbytheelectrostaticguideandtransportedtoanUHVchamberfor
detectionandfurtherexperiments.
Thedepletion-spectroscopytechniquedevelopedwithinthisthesisisemployedto
thequanptitativerformanceelystudyofintheternalsetup,cowhicolinghofcomthebinesmoleculesbuffer-gasinthecoolingbuffer-gasandcell.electrostaticInitially,
guiding,depletionhasspbeenectroscopyoptimizedofwguidedithdeuteratedformaldehydeammon(H2iaCO)(ND3)molecules,molecules.whichThereuphadboeenn,
cooledinthebuffer-gascellpriortoinjectionintotheelectricguide,wasperformed.
isInthisobtainedexpaserimenshotwndirectinFig.evidence7.2.forWhencotheolingoftemptheeratureinternalofthedegreesbuffer-gasofcellfreedomis
seekingreduced,morerotationalandstatemorepwithaopulationreasonablyaccumlargeulatesStarkintheshiftlo|wJ=1,est-energeticKa=1,loKc=w-field-0.
Hence,thepurityoftheguidedbeamissignificantlyimprovedbythelowtemper-
stateature|1of,1,the0conbuffer-gastributescell.2%Ftoorthecomparison,guidedbateam,aandsourceatatemptemperatureeratureofof300150KKtheit
contributes4%.Bycoolingthereservoir,fromwhichthemoleculesareextracted,
tocan4bKeandenhancedutilizingto80the%[Som09buffer-gas-co,vB09].olingThistechnique,demonstrathetesconthatbtributionyofcomplementhistinstateg

7.2OngoingdevelopmentsintheRempegroup

105

Figure7.3:Schematicrepresentationoftheopto-electricalcoolingprocess.Indicated
arethepotentialenergycurvesforthelfsmolecularstates|sand|wintheregionoflow
(left)andhighelectric-fieldstrength(right).(1)Moleculesinthestronglow-field-seeking
state|smovefromthelow-fieldtothehigh-fieldregion,loosingtheamountofkinetic
energycorrespondingtothedifferenceinStarkenergy.(2)There,theyarecoupledto
theweaklow-field-seekingstate|wbyamicrowavefield(µ-W),whichremovespotential
energy.(3)Themoleculesinstate|wmovebacktothelow-fieldregion,gainingless
kineticenergythantheylostduring(1).(4)Toclosethecycle,themoleculesareoptically
pumpedbyaninfraredlightfield(IR)toavibrationallyexcitedstate|e,(5)fromwhich
theycanspontaneouslydecaybacktotheinitialstate|s.

theelectrostaticvelocity-filteringsetupwithsuchacoldmoleculesourcebasedon
cryogenicbuffer-gascooling,high-flux,state-selected,coldguidedbeamsofpolar
moleculesareproduced.Furtherexperimentsutilizingthesecoldbeams,thetech-
nicaldetailsofthesetup,itsoptimizationwithrespecttotherelevantquantitiesof
theguidedbeam,anditseverydayoperationwillbedescribedinthedoctoralthesis
er.SommChristianof

7.2.2Opto-electricalcoolingofpolarmolecules
Ttecocohniqueolthetoevenmoleculeslowerprotempducederatures,bytheanewelectrostatictrappingveloandcitcoolingy-filteringschemeandisguidingunder
developmentintheRempegroup[Zep09].Itsprincipleisschematicallyshownin
Fig.7.3.Coldpolarmoleculesfromtheelectricguideareloadedintoanelectrostatic
trap.There,themoleculesareenclosedbyhighelectricfieldsprovidedbyaring
electrodeandtwoopposingmicrostructuredplateelectrodes.Thisgeometryresults
inatrappingpotentialforlow-field-seekingstates.
Inthetrapvolume,tworegionsofhomogeneous,butdifferentmagnitude,electric
fieldsarecreated,betweenwhichthemoleculescanfreelymove.Whenamolecule
movesfromthelow-fieldregiontothehigh-fieldregion,itloosestheamountof
kineticenergycorrespondingtothedifferenceinStarkenergy.Hence,thisenergy
fromdifferencethecanhigh-fielbedastohightheaslo1K.w-fieldSinceregion,thenocomoleculeolingcan,isacofhievcourse,ed.movebackagain

106

okOutlo

Toprovidecooling,adissipativeprocessmustbeaddedtothescheme.Thisis
accomplishedbyconsideringspontaneousvibrationaldecayinathree-levelsystem
asshowninFig.7.3.Inthehigh-fieldregion,thestrong|sandtheweak|w
low-field-seekingstatesarecoupled.Forpolarmolecules,thestates|sand|w
representdifferentrotationalenergylevels.Inthiscase,thecouplingisprovided
byamicrowavefield(µ-W).Themoleculeinstate|wcanmovefromthehigh-
fieldregiontothelow-fieldregion,therebygaininglesskineticenergythenitlost
whenclimbingthepotential-energyhillinstate|s.Inthelow-fieldregionthe
moleculeinstate|wisthenopticallypumpedtoanexcitedstate|e.Thefollowing
spontaneousdecaytotheinitialstate|srendersthewholeprocessunidirectional,
hencepermittinganetcoolingofthemoleculesinthetrap.
Notethattherequirementsforthisspontaneousdecayprocessinopto-electrical
coolingaredifferentfromthoseinconventionallasercooling.Lasercoolingrelies
oniterativesmallmomentumtransferbyscatteringphotonsonaclosedcycling
transition,thereforedemandingforafastdecayrateintheMHzrangeasfound
forelectronicdipoletransitions[Met99].Incontrast,opto-electricalcoolingbenefits
fromthelargeamountofenergythatisremovedperscatteredphoton.Thisallows
toreconsidertheuseofvibrationaltransitions,whichhavebeenneglectedforlaser
coolingduetoglacialdecayratesontheorderof100Hz.Sincevibrationaltransi-
tionsexhibitveryfavorableselectionrulesforsymmetric-topmolecules,theiruseis
envisionedfortheimplementationofthecoolingscheme.Simulationsofthecooling
processshowthepotentialtoreachatemperatureof1mKafter10s,whenstarting
withamolecularensembleatatemperatureof0.4K.Detailsoftheopto-electrical
coolingschemeaswellasexperimentaleffortstorealizethisideawillbediscussed
inthedoctoralthesisofMartinZeppenfeld.

AendixApp

reconstructionGuiding-efficiencyforthedifferentwaterisotopologs

Thepurposeofthisappendixistoexplainhowtheguidingefficienciesofthedifferent
waterisotopologsareextractedfromtheQMSsignal.Complicationsarisesincepure
measurementsareonlypossiblewithH2OandD2O.Forguidingexperimentswith
HDOamixtureofliquidH2OandD2Oispreparedinacontainer.Thesereactto
HDO,formH2O+D2O2HDO.(A.1)
Theequilibriumconcentrationsinthishydrogen-exchangereactiondependonthe
initialvolumeratioofH2OandD2O.Therefore,theconcentrationsofthethree
isotopologsinthisliquiddependonthechosenvolumeratiobetweenH2OandD2O.
Theconstituentsofthegasphaseabovethisliquid,whoseconcentrationsreflectthe
onesintheliquidphase,arebroughttothenozzlethroughaflowvalve,asdescribed
.2.2sectioninThemeasurementshaveallbeenperformedataconstantreservoirpressureof
0.10mbarwiththenozzleassemblyatroomtemperature.Toobtainsignalsof
allthreewaterisotopologs,severalmixtureswithdifferentvolumeratiosofH2O
andD2Ohavebeenprepared.Theseratiosandtheexperimentallydetermined
concentrationsintheequilibriumofthehydrogen-exchangereaction,Eq.(A.1),are
listedinTbl.A.1.Toreconstructthefluxesofguidedmoleculesfortheindividual
isotopologs,twomainquestionsmustbeanswered.Whatisactuallyinjectedinto
theguide,andwhatdetectorresponseisobtainedforoneguidedH2O,D2O,orHDO
.elyectivrespmolecule

A.1Concentrationsofwaterisotopologsinjected
intothequadrupoleguide
Tomonitorthegascontentsinjectedthroughtheceramicnozzle,aresidual-gas
analyzer(RGA)isplacedinthevacuumchambercontainingthenozzleandthe

107

108Guiding-efficiencyreconstructionforthedifferentwaterisotopologs

PreparedMixtureMeasuredContribution(%)
Meas.Nr.D2OH2OD2OHDOH2O
10100100
2109361
311224731
44132770
TableA.1:Volumeratiosofthedifferentliquidwaterisotopologswhichweremixed
inthetesttube,andtheresultingcontributionsoftheisotopologsinthegaseffusing
outofthenozzle.Inmeasurement2,whereonlyD2Owasputinthecontainer,the
contributionsofHDOandH2OareduetocontaminationsofthegaslineswithH2Ofrom
ts.measuremenprevious

(A.2b)

vfirstantbendmassesoftheduringthequadrupmoleeasuremenguide.ts.TheRBecauseGAtherecordsmoleculestheioncancurrenfragmentsoftallduringrele-
masselectron-impactunit,1amu=1ionization.66×10the−27ionkg),curren19amtsu,andmeasured20amatudomassnot18amudirectly(amu:reflectatomicthe
concentrationsofH2O,HDO,andD2O,respectively.Thefollowingfragmentsare
detectedintheRGA:H2O+18amu
H2O→OH++17amu(A.2a)
O+16amu
uam18ODHDO+19amu
HDO→OH+17amu(A.2b)
O+16amu
D2O+20amu
uam16OD2O→OD++18amu(A.2c)
Forallthesemolecules,alsohydrogen(H2+,H+)ordeuteriumions(D2+,D+)are
produced.However,duetothelargercontributionofbackgroundgasatthese
sevmasseseralwtheyaterareisotopnotologsusedcanforcondatatributetoacquisition.theRGAAscansignalbeexceptseenforfrom19Eq.am(uA.2and),
20amu.Therefore,somecorrectionsarenecessarytoreconstructtheconcentrations
oftheindividualwaterisotopologsfromthisintegralRGAsignal.
Inafirstmeasurement,pureliquidH2Owasused.Fromthemeasuredioncurrents
ofratiotationfragmena18amu80%
H2O→17amu19%(A.3)
16amu1%

A.1Concentrationsofwaterisotopologsinjectedintothequadrupoleguide109

isdetermined.Inasecondmeasurement,pureliquidD2Owasputinthecontainer
andthevaporwasinjectedthroughthenozzle.Nonetheless,alsocontributionsat
mass19amuand17amuaredetectedwiththeRGA.Theseunwantedcontamina-
tionscanbeattributedtoresidualH2Ofromthepreviousmeasurementssticking
tothewallsofthegaslines.TheH2OmoleculescanthenformHDObyhydrogen-
exchangereactionswithD2O.Thereforeitisnotpossibletoextractafragmenta-
tionratioforD2Ofromunperturbeddata.SubtractingthecontributionofHDO
byscalingthedataatmass19amuwithahypotheticalfragmentdistribution(see
Eq.(A.5)),thedatasuggestasimilarfragmentationratioofD2OasforH2O,
20amu80%
%1uam16D2O→18amu19%.(A.4)
SincethefragmentationratioofHDOcannotbedetermineduniquelyfromthe
residual-gas-analyzersignalduetothecontributionsofD2Oatmass18andH2Oat
mass16,basedonthemeasurementswithH2OandD2Othefragmentationratio
19amu80%
18amu9.5%
HDO→17amu9.5%(A.5)
16amu1%
assumed.isForthestudiesofthevelocity-filteringandguidingpropertiesofthewateriso-
topologs,mixtureswithdifferentvolumeratiosofH2OandD2Ohavebeenused.
TheseratiosandtheresultingcontributionsofD2O,HDO,andH2Otothegasare
listedinTbl.A.1.FormeasurementswiththemixturesofH2OandD2Oprepared
inthecontainer,thefollowingprocedurehasbeenusedtodeterminetherelative
contentsofthegasinjectedintotheguide.
•Thereservoirpressureforallthemeasurementsiskeptfixedat0.1mbar.
•Fromtheioncurrentmeasuredat20amu,I20,thetotalioncurrentofDDO2O,
ID2O,canbedirectlydeterminedusingthefragmentationprobabilityp202of
D2Ointomass20amu,Eq.(A.3),as
ID2O=1/p20D2O×I20.(A.6)
Similarly,themeasurementat19amu,I19,yieldsthetotalioncurrent
IHDO=1/p19HDO×I19(A.7)

HDO.of

110

Guiding-efficiencyreconstructionforthedifferentwaterisotopologs

FigureA.1:Electrode-voltagedependenceofthesignalofguidedD2OandHDOmo-
lecules.DifferentvolumeratiosofH2OandD2Ohavebeenputinthecontainer.The
measurementwiththeH2O:D2O=1:1mixtureistakenasareference.Thedatamea-
suredwiththeH2O:D2O=4:1mixtureareindividuallyscaledwiththecontributions
ofD2OandHDO(seeTbl.A.1)determinedwiththeRGAinthesourcevacuumchamber.

•ThetotalioncurrentofH2Ocanbedeterminedfromthemeasurementat
18amuusingthepreviouslydeterminedvaluesforthetotalioncurrentsof
D2OandHDO.Consideringthedifferentpossiblecontributionsat18amu,
findsoneI18=p18D2O×ID2O+p18HDO×IHDO+pH182O×IH2O,(A.8)
ansthereforearrivesat
IH2O=1/pH182OI18−p18D2O×ID2O+p18HDO×IHDO
=1/pH182OI18−p18D2O/p20D2O×I20+p18HDO/p19HDO×I19.(A.9)
•Asaconsistencycheck,theioncurrentsat17amuand16amucanbeused.
Totestthedependenceofelectrostaticvelocityfilteringandguidingontheamount
ofthedifferentisotopologsinjectedthroughthenozzle,theQMSsignalsofguided
HDOandD2Omoleculesdetectedatmass19amuand20amu,respectively,are
considered.Forthesemeasurements,H2OandD2Ohavebeenmixedinthesourc
withtwodifferentratios.TheQMSsignalsmeasuredwiththeH2O:D2O=1:1
mixtureservesasareference.Theobservedsignalsofguidedmoleculesusingthe
H2O:D2O=4:1mixturearethenscaledwithcontributionofHDOandD2Ode-
terminedwiththeRGAinthesourcevacuumchamber,whichreflecttheirrelative
fractiontothegasinjectedintheguide.AscanbeseenfromFig.A.1,theQMS
signalsofguidedHDOandD2Ocanbescaledwiththeioncurrent.Theremaining
differenceof5–10%mightbecausedbychangesinthebackgroundgasorbynon-
linearitiesoftheRGAandgiveanestimatefortheaccuracyofthedetermination
ofthegascontents.

A.2Detectionofcoldguidedwaterisotopologs

111

A.2Detectionofcoldguidedwaterisotopologs
Afterhavingdiscussedthedeterminationofthegascontentsinjectedintotheguide,
thesecondpointisaddressed,namelythedetectorresponsetotheguidedmolecules.
Forthesemeasurements,oneassumptionismade:Allthewaterisotopologshavethe
sametotalionizationprobability,whichseemsreasonableconsideringthesimilarity
ofthemolecules.Forthesemeasurementsthemasses16–20amuareconsideredas
forthedeterminationofthegascontentsinjectedintotheguide
FigureA.2showsthedistributionofmasses,atwhichfragmentsofguidedwater
moleculesaredetected.Inthisfigure,measurementswithvariousconcentrationsof
thewaterisotopologsinjectedintotheguidearecombined.Theseallowarecon-
structionofthedistributionsofthefragmentsfortheindividualwaterisotopologs.

(A.10)

•Fromthefirstmeasurement,Fig.A.2(a),whereonlyH2Owasinjectedinto
theguide,thefragmentdistributionofH2O
18amu63%
H2O→17amu19%(A.10)
16amu18%
visible.directlyis•ThemeasurementwithmainlyD2Oinjectedintotheguide,Fig.A.2(b),does
thenotconallowtotributiondirectlyofHDOtoreconstructthegastheinjectedfragmeninttothedistributionguideofthrouD2ghO.thenoAlthoughzzle
isnearlyonly6the%,samethecounQMSstrateignalasatthe19signalamu,atwhere20amu,onlywhicHDOhisconsolelytributes,causedgivbesy
higherguidedD2guidingOmeffiolecules.ciencydueThetoreasonitslargerforthisandlinearstrongStarkHDOconshifts.tributionisits
•FromthedatashowninFig.A.2(c),whereHDOwasinjectedwiththelargest
contributionof47%intotheguide,thefragmentationratioofHDOisex-
tracted.Becausethecountrateat20amuismuchsmallerthanthecount
rateat19amu,thecontributionofD2Oisneglectedfortheanalysis.Alsothe
influenceofHOisneglected,sinceitcontributeswithafractionsimilarto
thatofD2Oto2thegasinjectedintotheguideandisguidedwithanefficiency
comparabletothatofD2O.Thedistributionofmassesinthismeasurement
isthereforeuseddirectlyasafragmentationratioforHDO,
%16uam1819amu74%
HDO→17amu8%.(A.11)
16amu2%

(A.11)

112

Guiding-efficiency

reconstruction

for

the

tdifferen

aterw

ologsisotop

FigureA.2:Distributionofmasses,atwhichfragmentsofguidedH2O,D2O,andHDO
0.1mmoleculesbarhasarebeendetecused,tedatbutantheelectrogasdeconvtentsoltagehavofeb±5eenkV.vAariedasconstanshotwnreservinTbl.oirpA.1res.surFeromof
thesemeasurements,thefragmentationratiosforthevariousisotopologsarereconstructed.

A.2Detectionofcoldguidedwaterisotopologs

113

FigureA.3:DeterminationofthefragmentationratioofguidedD2Omolecules.The
insameadvdataance,aretheshoconwnastributioninFig.ofA.2guided(b).HDOUsingthemoleculesfragmentothetationsignalratioatofmassesHDO16–19determinedamu
subtracted.is

•TomeasuremenextracttthewithfragmenmainlytDdistributioO,Fig.nofA.2guided(b),Dare2Orevisitemoleculesd.Inthethisdataofmeasure-the
2H2menOt,conthetribdutedistributiononlyof1%tomassesthegasshowsinjectedfragmenintotsoftheHDOguide,anditsD2O.influenceSincise
neglectedhere.UsingtheextractedfragmentationratioofHDO,thecontribu-
oftionthisofguidedcorrectionHDOisshownmoleculesinFig.isA.3subtractedandyieldsfromathedfragmentistribution.distributionTheofresult

20amu72%
D2O→18amu21%(A.12)
16amu7%
forD2O.Notethatafterthecorrectiontheresidualsignalat17amuisconsis-
tentwithzero.BecauseonlyHDOcouldfragmentintothismass,thisgivesa
hintforthereliabilityofthemethod.

114

Guiding-efficiency

reconstruction

for

the

tdifferen

aterw

isotop

ologs

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Cavity-EnhancedRayleighScattering
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Internal-statethermometrybydepletionspectroscopyinacoldguided
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Danksagung

ZumsprecSchen,hlussdiemauf¨ochtevielfic¨haltigedieWGelegeisezumenheitnGelingenutzen,alldieserdenjenigenArbeitbeigemeinentragenDankhabauszu-en.

AnersterStellem¨ochteichmeinemDoktorvaterProf.Dr.GerhardRempef¨ur
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