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

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CHEVY et al. PHYSICAL REVIEW A 71, 062710 �2005� �10� C. H. Schunck, M. W. Zwierlein, C. A. Stan, S. M. F. Raupach, W. Ketterle, A. Simoni, E. Tiesinga, C. J. Williams, and P. S. Julienne, e-print cond-mat/0407373. �11� T. L. Ho and N. Zahariev, e-print cond-mat/0408469; T. L. Ho and R. B. Diener, e-print cond-mat/0408468. �12� Y. Ohashi, e-print cond-mat/0410516. �13� J. R. Taylor, Scattering Theory �John Wiley, New York, 1972�; H. Feshbach, Theoretical Nuclear Physics �John Wiley, New York, 1992�. �14� C. Chin, V. Vuletic, A. J. Kerman, and S. Chu, Phys. Rev. Lett. 85, 2717 �2000�; P. J. Leo, C. J. Williams, and P. S. Julienne, ibid. 85, 2721 �2000�. �15� Thomas Volz, Stephan Drr, Niels Syassen, Gerhard Rempe, Eric van Kempen, and Servaas Kokkelmans, e-print cond-mat/ 0410083. �16� A. R. Edmunds, Angular Momentum in Quantum Mechanics �Princeton University Princeton, NJ, Press, 1996�. �17� C. Ticknor, C. A. Regal, D. S. Jin, and J. L. Bohn, Phys. Rev. A 69, 042712 �2004�. 062710-8 �18� E. G. M. van Kempen, B. Marcelis, and S. J. J. M. F. Kokkelmans, e-print cond-mat/0406722. �19� For the sake of simplicity, these averaged parameters only were presented in �9�. �20� K. Dieckmann, C. A. Stan, S. Gupta, Z. Hadzibabic, C. H. Schunck, and W. Ketterle, Phys. Rev. Lett. 89, 203201 �2002�. �21� H. T. C. Stoof, J. M. V. A. Koelman, and B. J. Verhaar, Phys. Rev. B 38, 4688 �1988�. �22� Note that the different lifetimes calculated for the three m l states do not violate any rotational symmetry. Indeed, the magnetic field used to reach the Feshbach resonance provides a preferred direction to the system. �23� We evaluate R e by identifying it with the relative distance r at which the total �centrifugal + long-range� potential 3� 2 /mr 2 −C 6/r 6 −C 8/r 8 −C 10/r 10 cancels and we used the C 8,9,10 coefficients of �24�. Z.-C. Yan et al., Phys. Rev. A 54, 2824 �1996�. �24� C. Chin and R. Grimm �private communication�.
A.5 Expansion of an ultra-cold lithium gas in the BEC-BCS crossover LETICIA TARRUELL, MARTIN TEICHMANN, JASON MCKEEVER, THOMAS BOURDEL, JULIEN CUBIZOLLES, LEV KHAYKOVICH, JING ZHANG, NIR NAVON, FRÉDÉRIC CHEVY, CHRISTOPHE SALOMON, Proceedings of the 2006 Enrico Fermi summer school on Fermi gases, Varenna 2006. 151
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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
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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
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 and 108: 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 147 and 148: RESONANT SCATTERING PROPERTIES CLOS
Page 149: RESONANT SCATTERING PROPERTIES CLOS
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
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