One-dimensional Bose gas on an atom chip van Amerongen, AH

126 Pages·2017·2.82 MB·English

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One-dimensional Bose gas on an atom chip
van Amerongen, A.H.
Publication date
2008
Document Version
Final published version
Link to publication
Citation for published version (APA):
van Amerongen, A. H. (2008). One-dimensional Bose gas on an atom chip. [Thesis, fully
internal, Universiteit van Amsterdam].
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Download date:15 Feb 2023
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ISBN 978-90-9022841-9
One-dimensional Bose gas
on an atom chip

One-dimensional Bose gas
on an atom chip
ACADEMISCH PROEFSCHRIFT
ter verkrijging van de graad van doctor
aan de Universiteit van Amsterdam
op gezag van de Rector Magnificus
prof.dr. D.C. van den Boom
ten overstaan van een door het college voor promoties ingestelde
commissie, in het openbaar te verdedigen in de Agnietenkapel
op vrijdag 30 mei 2008, te 14:00 uur
door
Aaldert Hidde van Amerongen
geboren te Amsterdam
Promotiecommissie:
Promotor: prof.dr. J.T.M. Walraven
Copromotor: dr. N.J. van Druten
Overige leden: prof.dr. A. Aspect
prof.dr. M.S. Golden
prof.dr. H.B. van Linden van den Heuvell
prof.dr. K.J. Schoutens
prof.dr. G.V. Shlyapnikov
dr. R.J.C. Spreeuw
prof.dr. P. van der Straten
Faculteit der Natuurwetenschappen, Wiskunde en Informatica
ISBN: 978-90-9022841-9
The work described in this thesis was carried out
in the group “Quantum Gases & Quantum Information”, at the
Van der Waals-Zeeman Instituut of the University of Amsterdam,
Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands,
where a limited number of copies of this thesis is available.
A digital version of this thesis can be downloaded from
http://www.science.uva.nl/research/aplp
Funding was also provided by NWO (VIDI grant N.J. van Druten),
FOM (Projectruimte and program ’Quantum Gases’) and the EU
(Marie Curie Research and Training Network ’Atom Chips’).
Contents
1 Introduction 1
1.1 1D Bose gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Integrated atom optics . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 This thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Theoretical background 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Magnetic trapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Ideal Bose gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Ideal Bose gas harmonically trapped in 3D and 1D . . . . . . 10
2.3.2 Ideal Bose gas in the 3D-1D cross-over . . . . . . . . . . . . . 11
2.4 Weakly interacting (quasi-)condensate . . . . . . . . . . . . . . . . . 11
2.4.1 Mean-field 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.2 Mean-field 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.3 Mean-field 3D-1D crossover . . . . . . . . . . . . . . . . . . . 13
2.4.4 Excitations in elongated quasi-condensates . . . . . . . . . . . 14
2.5 Exact solutions in 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.1 Tonks-Girardeau . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.2 Lieb-Liniger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.3 Yang-Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Overview of ultracold Bose gas regimes . . . . . . . . . . . . . . . . . 20
2.6.1 Regimes for T = 0 . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6.2 Regimes in 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 Previous models for T > 0 . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7.1 Semi-ideal Bose gas . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7.2 Self-consistent Hartree-Fock . . . . . . . . . . . . . . . . . . . 22
2.8 Evaporative cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Experimental Setup 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Design considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Microtrap for cold atoms . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 Layout and construction . . . . . . . . . . . . . . . . . . . . . 33
3.4 Thermal properties of the microtrap . . . . . . . . . . . . . . . . . . . 37
3.4.1 Thermal conduction – analytic approach . . . . . . . . . . . . 38
3.4.2 Thermal conduction – Finite Element Method . . . . . . . . . 40
3.5 Vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.6 Dispenser pulsed atom source . . . . . . . . . . . . . . . . . . . . . . 44
v
vi CONTENTS
3.7 Magnetic field coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.8 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.9 Imaging system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10 Experimental control . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.10.1 Output control . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.10.2 Radio frequency source . . . . . . . . . . . . . . . . . . . . . . 55
3.11 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4 Realizing Bose-Einstein condensation 57
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Trapping and cooling sequence . . . . . . . . . . . . . . . . . . . . . . 57
4.2.1 MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.2 Compressed MOT . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.3 Optical pumping . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.4 Minitrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.5 Z-trap – compression . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.6 Reaching BEC by evaporative cooling . . . . . . . . . . . . . . 60
4.2.7 BEC in the 3D-1D cross-over . . . . . . . . . . . . . . . . . . 61
4.3 Potential roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Focusing phase-fluctuating condensates 65
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Gaussian and nonideal optical beams and ABCD matrices . . . . . . 67
5.2.1 Paraxial wave equation and Huygens-Fresnel integral . . . . . 67
5.2.2 Nonideal beam . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Atom optics and ABCD matrices . . . . . . . . . . . . . . . . . . . . 70
5.3.1 Schro¨dinger equation and Wigner function . . . . . . . . . . . 70
5.3.2 ABCD matrices for matter waves . . . . . . . . . . . . . . . . 72
5.3.3 Temperature of a focused non-interacting gas . . . . . . . . . 76
5.4 Quasi-condensate as nonideal atomic beam . . . . . . . . . . . . . . . 77
5.5 Weakly interacting condensate in a time dependent trap . . . . . . . 79
5.6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.8 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6 Yang-Yang thermodynamics on an atom chip 91
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.3 In situ density profiles . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.4 In focus density profiles . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.5 Analysis and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.6 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 96
References 99
CONTENTS vii
Summary 111
Samenvatting 113
Nawoord 115
viii CONTENTS