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

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CHAPTER 6. CONCLUSIONS Stable molecules can be formed by preparing the gas around the unitarity point and slowly ramping down the magnetic field into the BEC region. In this thesis we present experimental measurements which show that this molecule creation also happens for fast sweep rates if the density of the gas is sufficiently high. This can occur when we switch off the magnetic field in order to take an absorption picture of a cloud in the crossover, and can disturb the measured distribution. The development of new data analysis methods allowed us to determine more precisely the temperature of the gas. We also presented an algorithm to deconvolute absorption images into the original three dimensional density distribution. The presented experiments have also shown that we are at the limits at what our setup is capable of. Therefore, we have started with the construction of a second generation experimental apparatus. We have installed a new laser system, which is more flexible and stable than its predecessor. The vacuum system was rebuilt in large parts, including a complete rebuild of the Zeeman slower. As a result, the loading rate of the atoms is now ten times higher than before, enabling us to increase the repetition rate of our experiment, leading to better statistics. At the same time we optimized the geometry of the magnetic traps, which will enable us to increase the number of trapped atoms by about an order of magnitude. A new imaging system for the magneto-optical trap is an important tool in the characterisation of the new setup. In the near future, we plan to set up an optical lattice in our system. An optical lattice is a standing wave overlapped with the atomic cloud. Similar to an optical dipole trap, atoms will be trapped in the intensity maxima of the standing wave. Many different configurations are possible. We can successively “freeze out” the spatial degrees of freedom, enabling us to study atomic gases in low dimensions. For bosons, optical lattices have already become a standard tool, we refer to reference [151] for a review. Optical lattices open the possiblity to experimentally realize theoretical many-body models, without the problems appearing in solid state physics, such as lattice defects or impurities. One example is the Fermi-Hubbard model. Hubbard proposed in 1963 a simple model for electrons in a lattice [152] whose Hamiltonian contains only two terms, a next-neighbor tunneling and an on-site interaction term. It is a very simple model, but exhibits phenomena like a metal-insulator transition, ferromagnetism or superconductivity. For a review we refer to reference [153]. This model is still a challenge to theoretical physics, as no complete solution has been found yet. 122
Cold fermions in optical lattices can be seen as a direct experimental implementation of this model [154]. Its bosonic counterpart has already been experimentally realized [155]. Pioneering experiments have been performed for fermions. The group in Florence studied transport phenomena in optical lattices [156]. The MIT group reported on evidence for superfluidity in a lattice [157]. We already mentioned the efforts made by the group in Hamburg to study Bose-Fermi mixtures in optical lattices in section 5.5, and the study of p-wave resonances in optical lattices in Zürich in section 5.6.3. We see that optical lattices are an exciting future project, which will lead to a merge of cold atoms and solid state physics. 123
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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
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 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: Chapter 6 Conclusions In this thesi
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
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Martin Teichmann Atomes de lithium-6 ultra froids dans la ... - TEL

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