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One-dimensional Bose gas on an atom chip
van Amerongen, A.H.
Publication date 2008
Link to publication
Citation for published version (APA):
van Amerongen, A. H. (2008). One-dimensional Bose gas on an atom chip.
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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 Schr¨odinger 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
Summary 111
Samenvatting 113
