Martin Teichmann Atomes de lithium-6 ultra froids dans la ... - TEL

More documents

Recommendations

Info

CHAPTER 5. EXPERIMENTAL RESULTS U w ith trap BEC r w ith out trap BEC Figure 5.15: Illustration of the model used in the text. The points represent the thermal cloud. They are trapped in a potential created by the BEC before the trap is switched off, and pushed outwards afterwards by the expanding BEC. n(r,p) ∝ (exp(β(H − µ)) − 1) −1 , with H being the Hamiltonian in the trap. Then we numerically integrate the path of each atom with the BEC as a time-varying potential. As we are deeply on the BEC side of the resonance, we can calculate the expansion of the cloud using the formulae of the last section, knowing that in this limit the polytropic exponent is just 1. The result of such a simulation is shown in figure 5.16. It is a simulation of a condensate of 1000 molecules and some 3000 atoms in the thermal cloud (technically, we simulated one million atoms and divided the result appropriately to get a smoother curve). The expansion time is 12 times the trap frequency period, corresponding to the example data shown in the background. Unfortunately, we had to change the parameters to get a curve that is similar to experimental data: we simulated a scattering length between molecules of a = 0,02aho, while the experiments are done at a = 0,1aho. The number of molecules is also much higher in the experiment, about 2 · 10 4 . Those discrepancies are probably due to neglecting the interactions between the molecules in the thermal cloud. Another possibility is that the cloud contains a fraction of unbound atoms. Further investigation in this problem will be necessary. 5.5 Heteronuclear Feshbach resonances After atoms had been successfully cooled and trapped, various efforts have been made to extend this field to ultra-cold molecules. This is not a simple task, as laser cooling is difficult to achieve, as the level 108
density (a. u.) 70 60 50 40 30 20 10 0 5.5. HETERONUCLEAR FESHBACH RESONANCES -10 0 50 100 distance = ¹ m 150 200 Figure 5.16: Simulation of a molecular Bose-Einstein condensate. The solid line is the atomic density, the dashed line is the thermal cloud. The points are experimental data. The data is taken at kFa ≈ 1. 109
Page 1 and 2:
École Normale Supérieure Laborato
Page 3 and 4:
Contents 1 Introduction 7 2 Theory
Page 5 and 6:
Acknowledgments This thesis would n
Page 7 and 8:
Chapter 1 Introduction “The inter
Page 9 and 10:
T c / T F 1 10 -2 10 -4 cold Fe rm
Page 11 and 12:
JILA, where they use magnetic field
Page 13 and 14:
Chapter 2 Theory Da steh’ ich nun
Page 15 and 16:
2.2. A REMINDER ON SCATTERING THEOR
Page 17 and 18:
2.2. A REMINDER ON SCATTERING THEOR
Page 19 and 20:
pote ntial e ne rgy or probability
Page 21 and 22:
2.3. FESHBACH RESONANCES a total an
Page 23 and 24:
energy / mRy 2.0 1.5 1.0 0.5 0.0 -0
Page 25 and 26:
E / GH z 0,0 -0,5 -1,0 -1,5 -2,0 0
Page 27 and 28:
2.3. FESHBACH RESONANCES relating t
Page 29 and 30:
2.3. FESHBACH RESONANCES to fit the
Page 31 and 32:
second quantization, this is writte
Page 33 and 34:
equation (2.30) can easily be calcu
Page 35 and 36:
2.4. BCS THEORY Using the substitut
Page 37 and 38:
occupation probability 1.0 0.8 0.6
Page 39 and 40:
2.4. BCS THEORY loose the last smal
Page 41 and 42:
Chapter 3 Experimental setup LASER,
Page 43 and 44:
3.1. THE VACUUM CHAMBER Figure 3.1:
Page 45 and 46:
3.2. THE ZEEMAN SLOWER Figure 3.2:
Page 47 and 48:
3.3 The laser system 3.3. THE LASER
Page 49 and 50:
2 2 P 3/2 10 GH z 2 2 P 1/2 671 nm
Page 51 and 52:
input to Fabry- Pérot input non-po
Page 53 and 54:
7 P Am p to m agnetic trap im aging
Page 55 and 56:
atom ic be am pinch coils M O T coi
Page 57 and 58: 3.5. THE OPTICAL DIPOLE TRAP The he
Page 59 and 60: heating time / s 10 4 10 3 10 2 10
Page 61 and 62: Physics laser for the vertical. 3.6
Page 63 and 64: frequency / MHz 1000 950 900 850 3.
Page 65 and 66: 3.6. THE COOLING STRATEGY atoms in
Page 67 and 68: 3.7 MOT imaging 3.7. MOT IMAGING Wh
Page 69 and 70: 3.8. COMPUTER CONTROL where the cod
Page 71 and 72: from scipy.special import erf from
Page 73 and 74: Chapter 4 Data analysis A correct d
Page 75 and 76: 4.1. DETERMINATION OF THE TEMPERATU
Page 77 and 78: optical density 14 12 10 4.1. DETER
Page 79 and 80: F T = T r o f e u l a v d e t t i f
Page 81 and 82: Chapter 5 Experimental results Well
Page 83 and 84: 5.1. MOMENTUM DISTRIBUTION Now we h
Page 85 and 86: 2 ¹h = ¹ 2 a m 2 6 5 4 3 2 1 0 -1
Page 87 and 88: 5.1. MOMENTUM DISTRIBUTION get na 3
Page 89 and 90: n( k) 3 F k 1.0 0.8 0.6 0.4 0.2 5.2
Page 91 and 92: n( k) 3 F k 1.0 0.8 0.6 0.4 0.2 0.0
Page 93 and 94: 5.3. HYDRODYNAMIC EXPANSION where A
Page 95 and 96: 5.3. HYDRODYNAMIC EXPANSION The sit
Page 97 and 98: 5.3. HYDRODYNAMIC EXPANSION and tak
Page 99 and 100: ° 0.67 0.66 0.65 0.64 0.63 0.62 0.
Page 101 and 102: ellipticity 1.6 1.4 1.2 1.0 0.8 clo
Page 103 and 104: Ellipticity 1.55 1.50 1.45 1.40 1.3
Page 105 and 106: ellipticity 1.4 1.3 1.2 1.1 1.0 0.9
Page 107: 5.4. MOLECULAR CONDENSATE last sect
Page 111 and 112: E / GH z 0 -1 -2 |1,1〉 ⊗ |1/2,-
Page 113 and 114: number of atoms / 1000 25 20 15 10
Page 115 and 116: 5.6. OTHER EXPERIMENTS AND OUTLOOK
Page 117 and 118: Tem perature T c 0 Sarm a Ph ase 5.
Page 119 and 120: 5.6. OTHER EXPERIMENTS AND OUTLOOK
Page 121 and 122: Chapter 6 Conclusions In this thesi
Page 123 and 124: Cold fermions in optical lattices c
Page 125 and 126: Appendix A Articles A.1 Experimenta
Page 127 and 128: VOLUME 93, NUMBER 5 FIG. 1. Onset o
Page 129 and 130: VOLUME 93, NUMBER 5 gas. The platea
Page 131 and 132: P-wave Feshbach resonances of ultra
Page 133 and 134: P-WAVE FESHBACH RESONANCES OF ULTRA
Page 135 and 136: A.3 Expansion of a lithium gas in t
Page 137 and 138: Ry/Rx = 2.0(1) is consistent with t
Page 139 and 140: × ��
Page 141 and 142: Bth (G) Bexp (G) 218 not seen 230 2
Page 143 and 144: Resonant scattering properties clos
Page 145 and 146: RESONANT SCATTERING PROPERTIES CLOS
Page 151 and 152: A.5 Expansion of an ultra-cold lith
Page 153 and 154: 2 L. Tarruell, et al. to image the
Page 155 and 156: 4 L. Tarruell, et al. of mean field
Page 157 and 158: 6 L. Tarruell, et al. The starting
Page 159 and 160:
8 L. Tarruell, et al. for 0.5 ms in
Page 161 and 162:
10 L. Tarruell, et al. [11] M. H. A
Page 163 and 164:
Appendix B Bibliography [1] H. VOGE
Page 165 and 166:
[29] M. BARTENSTEIN, A. ALTMEYER, S
Page 167 and 168:
[62] P. NOZIÈRES and S. SCHMITT-RI
Page 169 and 170:
[98] M. MARINI, F. PISTOLESI, and G
Page 171 and 172:
[131] S. STRINGARI, Collective Exci
Page 173 and 174:
173
show all

Martin Teichmann Atomes de lithium-6 ultra froids dans la ... - TEL

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?