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

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APPENDIX B. BIBLIOGRAPHY [46] H. A. BETHE, Theory of the Effective Range in Nuclear Scattering, Phys. Rev. 76 (1949), 38. [47] S. SIMONUCCI, P. PIERI, and G. C. STRINATI, Broad vs. narrow Fano-Feshbach resonances in the BCS-BEC crossover with trapped Fermi atoms, Europhys. Lett. 69 (2005), 713-718. [48] K. E. STRECKER, G. B. PARTRIDGE, and R. G. HULET, Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas, Phys. Rev. Lett. 91 (2003), 080406. [49] K. HUANG and C. N. YANG, Quantum-Mechanical Many-Body Problem with Hard-Sphere Interation, Phys. Rev. 105 (1957), 767. [50] Y. CASTIN, Basic theory tools for degenerate Fermi gases, Proceedings of the 2006 Enrico Fermi Summer School on “Ultracold Fermi gases”, Varenna, Italy, 2007, available at arXiv:cond-mat/0612613. [51] D. D. KONOWALOW, R. M. REGAN, and M. E. ROSENKRANTZ, The “most likely” potential energy curve for the lowest 3 Σ + u state of Li2, J. Chem. Phys. 81 (1984), 4534. [52] D. D. KONOWALOW and M. L. OLSON, The electronic structure and spectra of the X 1 Σ + g and A 1 Σ + u states of Li2, J. Chem. Phys. 71 (1979), 450. [53] H. FESHBACH, Unified Theory of Nuclear Reactions, Ann. Phys. (N. Y.) 5 (1958), 357. [54] U. FANO, Effects of Configuration Interaction on Intensities and Phase Shifts, Phys. Rev. 124 (1961), 1866. [55] C. CHIN, A simple model of Feshbach molecules (2005), available at arXiv:cond-mat/0506313v2. [56] J. T. M. WALRAVEN, Elements of Quantum Gases: Thermodynamic and Collisional Properties of Trapped Atomic Gases, 2006, unpublished., available at http://staff.science.uva.nl/~walraven/walraven/Publications_files/ LesHouches2006.pdf [57] B. MARCELIS, E. G. M. VAN KEMPEN, B. J. VERHAAR, and S. J. J. M. F. KOKKELMANS, Feshbach resonances with large background scattering length: Interplay with open-channel resonances, Phys. Rev. A 70 (2004), 012701. [58] M. BARTENSTEIN, A. ALTMEYER, S. RIEDL, R. GEURSEN, S. JOCHIM, C. CHIN, J. HECKER DENSCHLAG, and R. GRIMM, Precise Determination of 6 Li Cold Collision Parameters by Radio-Frequency Spectroscopy on Weakly Bound Molecules, Phys. Rev. Lett. 94 (2005), 103201. [59] D. M. EAGLES, Effective Masses in Zr-Doped Superconducting Ceramic SrTiO3, Phys. Rev. 178, 668. [60] A. J. LEGGET, Cooper Pairing in Spin-Polarized Fermi Systems, J. Phys. (Paris) C 41 (1980), 7. [61] C. A. R. SÁ DE MELO, M. RANDERIA, and J. R. ENGELBRECHT, Crossover from BCS to Bose Superconductivity: Transition Temperature and Time-Dependent Ginzburg-Landau Theory, Phys. Rev. Lett. 71 (1993), 3202. 166
[62] P. NOZIÈRES and S. SCHMITT-RINK, Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity, J. Low Temp. Phys. 59 (1985), 195. [63] K. TANAKA and F. MARSIGLIO, Even-odd and super-even effects in the attractive Hubbard model, Phys. Rev. B. 60 (1999), 3508. [64] G. BRUUN, Y. CASTIN, R. DUM, and K. BURNETT, BCS theory for trapped ultracold fermions, Euro. Phys. J. D 7 (2004), 433. [65] T. BOURDEL, Gaz de Fermi en interaction forte : Du condensat de molécules aux paires de Cooper, Ph.D. Thesis, Université Paris 6, 2004. [66] M. TINKHAM, Introduction to Superconductivity, Dover, Mineola, N.Y., 1996. [67] P. A. LEE, N. NAGAOSA, and X.-G. WEN, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78 (2006), 17. [68] Q. CHEN, J. STAJIC, S. TAN, and K. LEVIN, BCS–BEC crossover: From high temperature superconductors to ultracold superfluids, Phys. Rep. 412 (2005), 1. [69] A. PERALI, P. PIERI, L. PISANI, and G. C. STRINATI, BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms, Phys. Rev. Lett. 92 (2004), 220404. [70] G. E. ASTRAKHARCHIK, J. BORONAT, J. CASULLERAS, and S. GIORGINI, Momentum distribution and condensate fraction of a Fermi gas in the BCS-BEC crossover, Phys. Rev. Lett. 95 (2005), 230405. [71] J. CUBIZOLLES, Fermions et Bosons Dégénérés au Voisinage d’une Résonance de Feshbach : Production de Molécules et Solitons d’Ondes de Matière, Ph.D. Thesis, Université Paris 6, 2004. [72] M. BARTENSTEIN, A. ALTMEYER, S. RIEDL, S. JOCHIM, C. CHIN, J. HECKER DENSCHLAG, and R. GRIMM, Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas, Phys. Rev. Lett. 92 (2004), 120401. [73] M. BARTENSTEIN, From Molecules to Cooper Pairs: Experiments in the BEC-BCS Crossover, Ph.D. Thesis, Leopold-Franzens-Universität Innsbruck, 2005. [74] G. B. PARTRIDGE, W. LI, R. I. KAMAR, Y.-A. LIAO, and R. G. HULET, Pairing and Phase Separation in a Polarized Fermi Gas, Science 311 (2006), 503. [75] J. T. STEWART, J. P. GAEBLER, C. A. REGAL, and D. S. JIN, The potential energy of a 40 K Fermi gas in the BCS-BEC crossover, Phys. Rev. Lett. 97 (2006), 220406. [76] J. CARLSON, S.-Y. CHANG, V. R. PANDHARIPANDE, and K. E. SCHMIDT, Superfluid Fermi Gases with Large Scattering Length, Phys. Rev. Lett. 91 (2003), 050401. [77] J. CARLSON and S. REDDY, Asymmetric Two-Component Fermion Systems in Strong Coupling, Phys. Rev. Lett. 95 (2005), 060401. [78] A. PERALI, P. PIERI, and G. C. STRINATI, Quantitative Comparison between Theoretical Predictions and Experimental Results for the BCS-BEC Crossover, Phys. Rev. Lett. 93 (2004), 100404. [79] G. E. ASTRAKHARCHIK, J. BORNAT, J. CASULLERAS, and S. GIORGINI, Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study, Phys. Rev. Lett. 93 (2004), 200404. 167
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
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
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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
Page 35 and 36:
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
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density (a. u.) 70 60 50 40 30 20 1
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E / GH z 0 -1 -2 |1,1〉 ⊗ |1/2,-
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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: [29] M. BARTENSTEIN, A. ALTMEYER, S
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
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