Bose-Einstein condensates in magnetic double well potentials [Elektronische Ressource] / presented by Thorsten Schumm

English
217 Pages
Read an excerpt
Gain access to the library to view online
Learn more

Description

Dissertation submitted to the Combined Faculties for the Natural Sciences and for Mathematics of the Ruperto-Carola University of Heidelberg, Germany for the degree of Doctor of Natural Science presented by Dipl.-Phys. Thorsten Schumm born in: Berlin, Germany Oral examination: February 20th, 2006 Bose-Einstein condensates in Magnetic double well potentials Referees: Prof. Dr. Jörg Schmiedmayer Prof. Dr. Michel Brune ContentsIntroduction 5I BEC, double wells and magnetic microtrapsIntroduction 131 Bose-Einstein condensation 151.1 Thenon-interactingBosegas............................. 151.2 TheinteractingBosegasatzerotemperature.................... 191.3 Bose-Einsteincondensatesinelongatedtraps.................... 221.4 InterferenceoftwoBose-Einsteincondensates 282 Double well physics 332.1 Thestaticdoublewell................................. 332.2 Thedynamicdoublewell ............................... 423 Magnetic microtraps 453.1 Magnetictrappingofneutralatoms.......................... 453.2 TheIoffe-Pritchardtrap................................ 483.3 Wiretraps........................................ 503.4 Surfaceeffects...................................... 563.5 Randommagneticpotentials .............................

Subjects

Informations

Published by
Published 01 January 2006
Reads 14
Language English
Document size 7 MB
Report a problem

Dissertation
submitted to the
Combined Faculties for the Natural Sciences
and for Mathematics
of the Ruperto-Carola University of Heidelberg,
Germany
for the degree of
Doctor of Natural Science



























presented by
Dipl.-Phys. Thorsten Schumm
born in: Berlin, Germany
Oral examination: February 20th, 2006












Bose-Einstein condensates in
Magnetic double well potentials
































Referees: Prof. Dr. Jörg Schmiedmayer
Prof. Dr. Michel Brune
Contents
Introduction 5
I BEC, double wells and magnetic microtraps
Introduction 13
1 Bose-Einstein condensation 15
1.1 Thenon-interactingBosegas............................. 15
1.2 TheinteractingBosegasatzerotemperature.................... 19
1.3 Bose-Einsteincondensatesinelongatedtraps.................... 22
1.4 InterferenceoftwoBose-Einsteincondensates 28
2 Double well physics 33
2.1 Thestaticdoublewell................................. 33
2.2 Thedynamicdoublewell ............................... 42
3 Magnetic microtraps 45
3.1 Magnetictrappingofneutralatoms.......................... 45
3.2 TheIoffe-Pritchardtrap................................ 48
3.3 Wiretraps........................................ 50
3.4 Surfaceeffects...................................... 56
3.5 Randommagneticpotentials ............................. 58
II A double well created by nanofabricated wires
Introduction 69
4 Static magnetic double well potentials 71
4.1 Realizingthetwomodesmodel............................ 71
4.2 A1Ddoublewellbasedonmagneticmicrotraps................... 75
4.3 Stability of the double well .............................. 80
4.4 Chosenparameters................................... 83
5 Experimental implementation 85
5.1 AsinglelayeratomchipforBose-Einsteincondensation.............. 85
5.2 Adoublelayeratomchipforrealizingamagneticdoublewel........... 91
5.3 Experimentalsetup1006 Experimental results 109
6.1 Bose-Einsteincondensation..............................109
6.2 Studyofrandommagneticpotentials.........................116
6.3 Experimentsinamagneticdoublewel........................125
6.4 Outlook.........................................139
III A double well realized by adiabatic dressed potentials
Introduction 145
7 Adiabatic dressed double well potentials 147
7.1 Atoms in rapidly oscillating magnetic fields .....................147
7.2 Realizingadoublewelgeometry...........................151
7.3 Stability of the double well ..............................160
8 Experimental implementation 163
8.1 Ahybridmacroscopic-microscopicatomchip ....................163
8.2 Experimentalsetup...................................167
9 Experimental results 173
9.1 Bose-Einsteincondensation174
9.2 DynamicsplitingofaBECinanRFinduceddoublewelpotential .......176
9.3 Outlook.........................................188
Summary and conclusions
Annex: publications
References 203Introduction
HIS year, the world’s scientific community is celebrating the ”Year of Albert Einstein”,
referring to the centennial of three of his most famous publications in 1905; his work
T on special relativity [1], about the Brownian motion [2] and on quantum theory [3].
Since then, quantum phenomena have become experimentally accessible in almost any physical
system. Fundamental questions like the interpretation problem, the question of decoherence
and the measurement process can now be addressed experimentally and are still the driving
force behind research carried out today. Furthermore, quantum effects have become the building
blocks for applied sciences and technology, most prominent examples being the laser as a coherent
photon source, along with many effects in solid state systems, which build the basis of today’s
microelectronics. The enormous success of the laser and coherent optics in general has stimulated
research towards similar applications in other well controlled quantum systems. In close analogy
to coherent optics with photons, the field of atom optics has developed. At its heart, based on
Einsteins (and Boses) work of 1924/25 [4,5,6], the Bose-Einstein condensate (BEC) as coherent
matter wave source.
The specific properties of neutral atoms make them promising candidates for manipulation
on the quantum level. Their weak coupling to the (uncontrolled) environment on the one hand
allows for long coherence times of the quantum state and therefore the storage and manipulation
of information in external or internal atomic states. On the other hand, a numerous tools for
neutral atom manipulation has been developed, ranging from laser cooling, over various sorts of
conservative atom traps to evaporative cooling. The combination of these methods has enabled
Bose-Einstein condensation in 1995 [7, 8, 9]. Different from photons, inter-particle interaction
play an important role in the properties of the quantum state and can be manipulated at will
by the use of Feshbach resonances [10]. This high degree of control has enabled the use of atoms
as a test scenario for other, less accessible quantum systems, such as solid states or quantum
liquids [11].
In contrast to photons, atoms carry significant mass, making the atomic quantum system
extremely sensitive to gravity, accelerations and rotations. Interferometers based on external
(motional) atomic quantum states therefore have been proposed and experimentally demon-
strated [12]. However, most of these implementations are based on manipulation in momentum
space and lack total control over the wave packet in coordinate space.
Controlled splitting of a quantum wave function in a double well potential is the generic
testing ground for matter wave dynamics, realizing the analogy of a beam splitter in coherent
optics. A coherent matter wave beam splitter represents a basic element of cold atom optics
and has been a long standing goal. Furthermore, Bose-Einstein condensates in static double
well potentials represent a fascinating, yet basically unexplored system in itself: a weak tunnel
coupling permits the observation of macroscopic tunnel currents through a classically forbidden
region. Atom-atom interactions significantly affect the single well on-site energy and give rise
to new nonlinear oscillatory modes.
Controlling external atomic quantum states and transporting matter wave packets represents
a major experimental challenge, as the system has to be manipulated on its intrinsic length scale,usually on the order microns.
Magnetic trapping potentials created by current carrying wires, fabricated on atom chips
enable potential variations on the scale of the structure size. Micro fabrication techniques,
as employed in the production of commercial computer chips, consequently allow the creation
of micron size magnetic double well potentials using simple wire structures. The potential
barrier and trap separation can be controlled with great accuracy by controlling wire currents
and external fields. Additional forces acting on the trapped atoms can be implemented using
oscillating magnetic or static electric fields, locally generated on the atom chip. They can be
used to deliberately imbalance the double well, to initiate a tunnel dynamics, or to influence
the relative phase evolution in split condensates. By designing complex wire patterns, a double
well beam splitter can be combined with other atom optical elements, such as guides, phase
shifters and combiners, opening the perspective to totally integrated cold atom interferometers.
Ongoing experimental effort aims for also integrating the atom detection on the chip. The atom
chip approach has brought with it a significant simplification and miniaturization of the entire
experimental setup. Transportable units are currently being tested in drop towers and parabolic
flights.
This manuscript presents and compares two different approaches to realize a magnetic double
well potential on an atom chip. The Orsay group follows the concept of miniaturization in a
consequent manner and employs sub-micron wire structures in an improved, noise rejecting
trapping geometry. A new technique has been developed and implemented in the Heidelberg
group, which involves oscillating magnetic fields, resonantly coupling magnetic sub-states of the
trapped atoms and creating new potential shapes in the dressed adiabatic states. Starting from
the basic concepts, both approaches are theoretically investigated in particular regard to an
experimental implementation. Based on these feasibility studies, the individual experimental
setups have been designed or adapted. Both realizations of a magnetic double well potential
have been tested experimentally, first results will be presented in the dedicated parts of this
manuscript.
Orsay: A double well potential based on nanofabricated wire structures
In 2001, E. Hinds et.al. proposed to use magnetic fields created by two parallel current carrying
wires on an atom chip in combination with an external magnetic field to create a double well
potential for cold neutral atoms [13]. By adjusting field and currents, the double well separation
can be manipulated at will, both traps can be merged and separated, realizing a beam splitter for
Bose-Einstein condensates in the time domain. We analyzed this conceptually simple approach
under realistic experimental conditions and found it to be extremely sensitive to fluctuations
of external fields or wire currents [14]. Recent experimental observations reported in [15] seem
to approve our analysis. The initial two wire proposal was consequently extended to a self-
sustaining five wire geometry to realize a stable magnetic double well potential on an atom
chip. Even though a high degree of noise rejection can be obtained using this geometry, the
structure has do be miniaturized to the micron level, necessitating nanofabricated trapping
wires. Within our collaboration with the LPN in Marcoussis, a double layer atom chip has been
created, carrying wires of 700 nm cross section. This device has been integrated into the existing
atom chip setup, which had to be changed considerably to meet the high stability requirements
imposed by the envisaged experiments.
Heidelberg: A double well potential based on dressed adiabatic potentials
Equally in 2001, O. Zobay and B. Garraway proposed to couple internal Zeeman states of
magnetically trapped neutral atoms by a strong oscillating (RF) magnetic field and create new
potential shapes in the emerging dressed adiabatic potentials [16,17]. Their scheme assumes a(spatially) constant RF coupling strength and hence new potential minima are formed on the
iso-potential surface of the initial static magnetic trap.
By taking into account the spatially dependent coupling strength, we extend the original
proposal and demonstrate, that strongly confining double well potentials can be created using
dressed adiabatic potentials [18]. In combining the scheme with the atom chip approach, a
high level of control and stability is obtained. Drawing straighter benefit from the strong atomic
confinement provided by magnetic microtraps, this scheme can be implemented with comparably
large structure sizes, withdrawing the need for high-end nanofabrication technologies.
Temporal outline of the thesis
This thesis was carried out as a joined project (”Cotutelle de Th`ese”) at the Institut d’Optique
in Orsay and the Physikalisches Institut in Heidelberg. Thanks to the cooperation of my two
supervisors, C. Westbrook and J. Schmiedmayer, I had the opportunity to work on two of the
probably most promising approaches towards the experimental implementation of a quantum
beam splitter on an atom chip.
When starting the thesis on October 2002, the first generation of chip experiments in Orsay
was almost built up. From an operating surface magneto optical trap (MOT), a magnetic
trap provided by a current carrying chip wire was loaded and Bose-Einstein condensation was
achieved in May 2003. As almost any other group working with atom chips, we encountered the
phenomenon of fragmentation; a cold atom cloud or a BEC breaking up into lumps when brought
close to the trapping structure. A careful study of the underlying magnetic trapping potential
could explain this effect by current deviations in the chip wire due to fabrication defects [19].
This analysis was finished in winter 2003.
In order to create a stable magnetic double well to realize tunnelling and splitting of Bose
condensates, the experimental setup was modified considerably in the beginning of 2004. The
vacuum system was rebuilt to fit into a multi layer magnetic field shielding. A new generation
of atom chips was designed, employing a hybrid ”sandwich” technology and including different
methods of microfabrication (optical lithography followed by electroplating and direct electron
beam lithographie followed by lift off). This chip carries large pattern submicron structures,
involves patterned silicon etching, mechanical polishing and intra chip bonding. It’s design,
fabrication, loading with Bose condensed atoms and preliminary experiments constitute the main
part of my thesis work in Orsay and will be described in the second part of this manuscript.
The experiments carried out in Heidelberg were performed with a conceptually similar setup,
which was fully operational by the time I joined the group. Few electronic components had to
be added to create the desired oscillating magnetic (RF) fields. An additional imaging system
was installed to directly observe atoms in the double well potential. Due to the simplicity of
the beamsplitter concept employed in Heidelberg, experimental results, as a coherent splitting
of a BEC on an atom chip could be obtained in only 8 month time, distributed over 3 visiting
periods. Working out the beam splitter concept, it’s implementation and first experiments with
split condensates constitute the main part of my thesis work in Heidelberg and will be described
in the third part of this manuscript.
During the time of this thesis, two experimental approaches, both based on optical potentials,
have successfully realized a coherent splitting of a Bose Einstein condensate in a double well
potential [20]. Josephson plasma oscillations as well as macroscopic quantum self trapping have
been observed [21].
Structure of the manuscript
Part 1 of this manuscript is a general theoretical introduction to Bose-Einstein condensates
in double well potentials, created by magnetic microtraps. Chapter 1 briefly reviews theideal and the interacting Bose gas and the phase transition to BEC. Owing to the typical
elongated geometry of magnetic wire traps, the shape and coherence properties of Bose
condensates at the 1D-3D crossover are discussed. As the phase of the condensate wave
function becomes apparent in interferometric detection, interference of independent, and
of phase locked sources is described. Chapter 2 discusses the dynamics of the macroscopic
wave function in a double well potential. In the framework of the two modes approxi-
mation, analytic expressions for double well population and relative phase can be found.
Dynamic instabilities beyond the two modes model are discussed as well as the breakdown
of adiabaticity in the dynamic splitting of a Bose-Einstein condensate. Chapter 3 reviews
the technique of magnetic trapping of neutral atoms with special regard to microscopic
wire traps on atom chips. Surface effects induced by the presence of the atom chip as well
as magnetic disorder potentials, causing fragmentation of atomic clouds in the vicinity of
the trapping structure are discussed.
Part 2 describes the experimental approach to a stable magnetic double well potential on an
atom chip chosen in the Orsay group. Chapter 4 discusses the realization of the two
modes approximation using magnetic microtraps. An improved, noise rejecting trapping
geometry is developed and investigated under realistic experimental conditions. Based on
a stability analysis, optimal geometric dimensions are determined. The fabrication of the
designed device is presented in chapter 5, together with a description of the experimental
setup for the creation of a Bose-Einstein on the atom chip. Chapter 6 describes the
experimental sequence to create a BEC in this setup. A quantitative experimental study
on the phenomenon of fragmentation is performed, identifying its origin for our system. We
present loading of atoms to the nanofabricated trapping geometry and first experiments
in the double well potential.
Part 3 of the manuscript presents a new method to create double well potentials on atom chips,
implemented in the Heidelberg setup. It is based on dressed adiabatic potentials, that arise
when magnetic sub-states of trapped neutral atoms are resonantly coupled using oscillating
(RF) fields. The theory of dressed adiabatic potentials and their implementation
on atom chips is presented in chapter 7. To determine optimal wire dimensions, a stability
analysis is carried out, similar to the one presented in part 2. Chapter 8 describes the
experimental realization of the Heidelberg atom chip setup. Experimental results obtained
with Bose-Einstein condensates in the RF induced double well potential are presented in
chapter 9.
A summary of the obtained results as well as a comparison of both presented experimental
approaches can be found in the conclusion.