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

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Expansion of a lithium gas in the BEC-BCS crossover 9 Ellipticity 1.6 a 1.5 1.4 1.3 1.2 1.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0 -1/k a F Ellipticity 1.6 b 1.5 1.4 1.3 1.2 1.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0 -1/k a F Fig. 5. – Ellipticity of the gas after expansion from a trap of depth ∼ 1.8 TF (a) and from a trap of depth ∼ 1.6 TF (b). Solid lines: hydrodynamic predictions. expanding gas at finite temperature. 7. – Acknowledgments We gratefully acknowledge support by the IFRAF institute and the ACI Nanosciences 2004 NR 2019. We thank the ENS ultracold atoms group, S. Stringari, R. Combescot, D. Petrov and G. Shlyapnikov for stimulating discussions. Laboratoire Kastler Brossel is a research unit No. 8552 of CNRS, ENS, and Université Paris 6. REFERENCES [1] S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, Science, 302 (2003) 2101. [2] M. Greiner, C. A. Regal, and D. S. Jin, Nature, 426 (2003) 537. [3] T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F. Kokkelmans, and C. Salomon, Phys. Rev. Lett., 93 (2004) 050401. [4] M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett., 91 (2003) 250401. [5] J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, Phys. Rev. Lett., 92 (2004) 150402. [6] G. B. Partridge, K. E. Strecker, R. I. Kamar, M. W. Jack, and R. G. Hulet, Phys. Rev. Lett., 95 (2005) 020404. [7] D. M. Eagles, Phys. Rev., 186 (1969) 456. [8] A. J. Leggett, in Modern Trends in the Theory of Condensed Matter, Lecture Notes in Physics Vol. 115, edited by A. Pekalski and R. Przystawa, (Springer-Verlag, Berlin) 1980, p. 13. [9] P. Nozières and S. Schmitt-Rink, J. Low Temp. Phys., 59 (1985) 195. [10] E. Shuryak, Prog. Part. Nucl. Phys., 53 (2004) 273.
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Page 1 and 2:
École Normale Supérieure Laborato
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Contents 1 Introduction 7 2 Theory
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Acknowledgments This thesis would n
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Chapter 1 Introduction “The inter
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T c / T F 1 10 -2 10 -4 cold Fe rm
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JILA, where they use magnetic field
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Chapter 2 Theory Da steh’ ich nun
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2.2. A REMINDER ON SCATTERING THEOR
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2.2. A REMINDER ON SCATTERING THEOR
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pote ntial e ne rgy or probability
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2.3. FESHBACH RESONANCES a total an
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energy / mRy 2.0 1.5 1.0 0.5 0.0 -0
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E / GH z 0,0 -0,5 -1,0 -1,5 -2,0 0
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2.3. FESHBACH RESONANCES relating t
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2.3. FESHBACH RESONANCES to fit the
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second quantization, this is writte
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equation (2.30) can easily be calcu
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2.4. BCS THEORY Using the substitut
Page 37 and 38:
occupation probability 1.0 0.8 0.6
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2.4. BCS THEORY loose the last smal
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Chapter 3 Experimental setup LASER,
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3.1. THE VACUUM CHAMBER Figure 3.1:
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3.2. THE ZEEMAN SLOWER Figure 3.2:
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3.3 The laser system 3.3. THE LASER
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2 2 P 3/2 10 GH z 2 2 P 1/2 671 nm
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input to Fabry- Pérot input non-po
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7 P Am p to m agnetic trap im aging
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atom ic be am pinch coils M O T coi
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3.5. THE OPTICAL DIPOLE TRAP The he
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heating time / s 10 4 10 3 10 2 10
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Physics laser for the vertical. 3.6
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frequency / MHz 1000 950 900 850 3.
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3.6. THE COOLING STRATEGY atoms in
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3.7 MOT imaging 3.7. MOT IMAGING Wh
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3.8. COMPUTER CONTROL where the cod
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from scipy.special import erf from
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Chapter 4 Data analysis A correct d
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4.1. DETERMINATION OF THE TEMPERATU
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optical density 14 12 10 4.1. DETER
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F T = T r o f e u l a v d e t t i f
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Chapter 5 Experimental results Well
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5.1. MOMENTUM DISTRIBUTION Now we h
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2 ¹h = ¹ 2 a m 2 6 5 4 3 2 1 0 -1
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5.1. MOMENTUM DISTRIBUTION get na 3
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n( k) 3 F k 1.0 0.8 0.6 0.4 0.2 5.2
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n( k) 3 F k 1.0 0.8 0.6 0.4 0.2 0.0
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5.3. HYDRODYNAMIC EXPANSION where A
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5.3. HYDRODYNAMIC EXPANSION The sit
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5.3. HYDRODYNAMIC EXPANSION and tak
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° 0.67 0.66 0.65 0.64 0.63 0.62 0.
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ellipticity 1.6 1.4 1.2 1.0 0.8 clo
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Ellipticity 1.55 1.50 1.45 1.40 1.3
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ellipticity 1.4 1.3 1.2 1.1 1.0 0.9
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5.4. MOLECULAR CONDENSATE last sect
Page 109 and 110: density (a. u.) 70 60 50 40 30 20 1
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: 8 L. Tarruell, et al. for 0.5 ms in
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
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