Few-body physics in ultracold Fermi gases [Elektronische Ressource] / presented by Timo Bastian Ottenstein

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Dissertationsubmitted to theCombined Faculties of the Natural Sciences and forMathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural SciencesPresented byDiplom-Physiker Timo Bastian OttensteinBorn in EberbachOral examination: February 3rd, 2010Few-body physics in ultracold Fermi gasesReferees: Juniorprofessor Dr. Selim JochimProf. Dr. Matthias WeidemüllerAbstractThis thesis reports on experimental studies of few-body physics in ultracold Fermigases. The main part is devoted to the first realisation of an ultracold three-component Fermi gas in thermal equilibrium that consists of atoms in the three6lowest spin states of Li.In first experiments the collisional stability of the gas was investigated in de-pendence of the interparticle interaction. The interaction strength was tuned by anexternal magnetic field employing Feshbach resonances in all three two-body scat-tering channels. At two magnetic field values a resonant enhancement of three-body loss was observed that can be explained by an Efimov-like trimer consistingof one atom in each of the three states which crosses the continuum twice in thestudied magnetic field region. The behaviour of three-body loss rates could beunderstood by taking into account a variation of the lifetime of the trimer with themagnetic field.These experiments were performed with large ensembles of atoms.

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Dissertation
submitted to the
Combined Faculties of the Natural Sciences and for
Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
Presented by
Diplom-Physiker Timo Bastian Ottenstein
Born in Eberbach
Oral examination: February 3rd, 2010Few-body physics in ultracold Fermi gases
Referees: Juniorprofessor Dr. Selim Jochim
Prof. Dr. Matthias WeidemüllerAbstract
This thesis reports on experimental studies of few-body physics in ultracold Fermi
gases. The main part is devoted to the first realisation of an ultracold three-
component Fermi gas in thermal equilibrium that consists of atoms in the three
6lowest spin states of Li.
In first experiments the collisional stability of the gas was investigated in de-
pendence of the interparticle interaction. The interaction strength was tuned by an
external magnetic field employing Feshbach resonances in all three two-body scat-
tering channels. At two magnetic field values a resonant enhancement of three-
body loss was observed that can be explained by an Efimov-like trimer consisting
of one atom in each of the three states which crosses the continuum twice in the
studied magnetic field region. The behaviour of three-body loss rates could be
understood by taking into account a variation of the lifetime of the trimer with the
magnetic field.
These experiments were performed with large ensembles of atoms. A finite
deeply degenerate Fermi gas consisting of a controlled number of atoms may
serve as a clean model for finite Fermi systems as for example atomic nuclei.
An approach for the preparation of such a gas is discussed and first experimental
steps are presented.
Zusammenfassung
Diese Arbeit behandelt experimentelle Untersuchungen von Wenigteilchen-Phä-
nomenen in ultrakalten Fermigasen. Der Schwerpunkt liegt auf der ersten Re-
alisierung eines dreikomponentigen Fermigases im thermischen Gleichgewicht,
6welches aus Li Atomen in den niedrigsten drei Zeeman Zuständen besteht.
Feshbach-Resonanzen erlaubten es, durch Anlegen eines äusseren Magnetfeldes
die Stabilität des Gases in Abhängigkeit der Wechselwirkung zwischen den Atomen
zu untersuchen. Für zwei Magnetfeldwerte wurde eine resonante Überhöhung des
Dreikörperverlustes beobachtet, was durch einen universellen Trimerzustand erk-
lärbar ist, der bei diesen Magnetfeldwerten das Kontinuum kreuzt. Ein komplettes
Verständnis für den Verlauf der auftretenden Verlustraten konnte durch Berück-
sichtigung einer magnetfeldabhängigen Lebensdauer des Trimers gewonnen wer-
den.
Diese Experimente wurden in grossen Ensembles ultrakalter Atome durchge-
führt. Ein endliches Fermigas bestehend aus einer kontrollierbaren Anzahl von
Atomen wäre ein ideales Modellsystem für endliche fermionische Systeme, wie
zum Beispiel Atomkerne. Eine Methode zur Präparation eines solchen endlichen
Fermi Gases wird vorgestellt und die ersten bereits durchgeführten Schritte präsen-
tiert.Contents
1 Introduction 1
2 Ultracold Fermi gases 7
2.1 Ideal Fermi gas . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Elastic collisions . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Tuning interactions - Feshbach resonance . . . . . . . . . . . . . 12
2.4 Universality and unitarity in ultracold gases . . . . . . . . . . . . 14
3 Universal few-body physics in ultracold gases 19
3.1 Universal trimers - Efimov states . . . . . . . . . . . . . . . . . . 20
3.2 Theory of the three-body problem - The hyperspherical approach . 22
3.2.1 Hyperspherical coordinates . . . . . . . . . . . . . . . . . 22
3.2.2 Faddeev equations . . . . . . . . . . . . . . . . . . . . . 23
3.2.3 potentials . . . . . . . . . . . . . . . . . . 25
3.3 Three-body recombination in ultracold gases . . . . . . . . . . . . 26
3.3.1 Efimov’s radial law . . . . . . . . . . . . . . . . . . . . . 27
3.3.2 Three-body recombination into a shallow dimer . . . . . . 29
3.3.3 Effects of deep dimers . . . . . . . . . . . . . . . . . . . 31
3.3.4 Three-body for negative scattering lengths . 32
3.3.5 Thermal effects . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Experimental evidence for Efimov states . . . . . . . . . . . . . . 35
4 Experimental setup 39
4.1 Vacuum chamber . . . . . . . . . . . . . . . . . . . . . . . . . . 39
64.2 Laser cooling and imaging of Li atoms . . . . . . . . . . . . . . 42
4.2.1 Laser system . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.2 Zeeman slower . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.3 Magneto optical trap (MOT) . . . . . . . . . . . . . . . . 45
4.2.4 Imaging systems . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Optical dipole traps . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1 Setup of the large volume dipole trap . . . . . . . . . . . 59
i4.3.2 Time averaged potentials . . . . . . . . . . . . . . . . . . 61
4.3.3 The microtrap . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4 Feshbach coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.5 Manipulating spin states - the radio frequency (RF) setup . . . . . 69
4.6 Computer control of the experiment . . . . . . . . . . . . . . . . 71
65 Ready for experiments: Preparation of a BEC of Li molecules 732
5.1 Bose-Einstein condensation in ideal gases . . . . . . . . . . . . . 73
5.2 The condensed state in the presence of interactions . . . . . . . . 75
5.3 Evaporative cooling . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Molecule formation . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.5 Observation of Bose-Einstein condensation . . . . . . . . . . . . 80
6 From two to three: Experiments with three-component Fermi gases 83
6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Preparation of a three-component mixture . . . . . . . . . . . . . 85
6.3 Collisional stability . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.4 Measurement of three-body loss coefficients . . . . . . . . . . . . 90
6.5 Interpretation of the data . . . . . . . . . . . . . . . . . . . . . . 93
6.5.1 Scaling of three-body losses in a three-component Fermi
gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.5.2 A universal Efimov-like trimer . . . . . . . . . . . . . . . 96
6.5.3 Effects of dimers . . . . . . . . . . . . . . . . . . . . . . 98
66.6 Efimov physics in ultracold gases of Li atoms . . . . . . . . . . . 100
7 From the thermodynamic limit to physics in a finite system 105
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.2 Our approach towards a finite system of ultracold fermions . . . . 106
7.3 Spilling atoms from the microtrap - an estimate of tunneling rates 109
8 Approaching the finite Fermi gas: First experiments 115
8.1 The microtrap at work . . . . . . . . . . . . . . . . . . . . . . . 115
8.2 Spilling atoms from the microtrap . . . . . . . . . . . . . . . . . 117
8.3 Single atom detection using fluorescence imaging . . . . . . . . . 120
9 Conclusion and outlook 123
9.1 Three-component Fermi gases: A new playground . . . . . . . . . 123
9.2 Towards a finite system of ultracold fermions . . . . . . . . . . . 126
A Fundamental constants 129
6B Level scheme of Li 131
iiList of Figures 134
Bibliography 147
iiiiv