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

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CHAPTER 5. EXPERIMENTAL RESULTS n( k) 3 F k 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 noninteracting gas F a= ¡ unitarity limit k F k a= 3 3 0.1 molecules 0.0 0.0 0.5 1.0 k= k 1.5 2.0 Figure 5.2: The calculated momentum distributions in a harmonic trap. The curves are normalized to � ∞ 0 n(k)k2dk = 1. The areas under the curves are not equal as the number of atoms is proportional to the density multiplied by the surface of the sphere with radius k. kF is the Fermi wave vector calculated for the noninteracting gas. 86 F
5.1. MOMENTUM DISTRIBUTION get na 3 = 3π/16x 2 0 , or ∆2 = 4¯h 4 k 3 F /3πm2 a. Then from (5.4) we see that µ = −¯h 2 /2ma 2 . This is exactly the molecular binding energy per atom that has been found in equation (2.25). Developing the summands in the number equation (2.35) for small values of ∆/µ, in combination with the result from this paragraph, leads to nk = 4 3 1 (kFa) 3π (k2a2 + 1) 2 (5.6) This result is interesting as it is the Fourier transform of a molecular bound state. This means that the center of mass motion of the molecules is condensed into p = 0 and only the relative motion of the atoms in the molecule is relevant. This shows that in the BEC limit the BCS wavefunction indeed describes a Bose-Einstein-Condensate of molecules. 5.1.4 Experiments We measure the momentum distribution at three different magnetic fields: at the unitarity limit at 83 mT, in the molecular regime and on the BCS side of the Feshbach resonance. We perform evaporative cooling as described in section 3.6. At the end of this cooling stage we lower both trapping lasers to 10% of their initial power, leading to transverse trapping frequencies of 2 kHz in both the horizontal and vertical beam. The desired field is then ramped in 500 ms to the desired magnetic field. At this point we would like to verify that we are indeed sufficiently cold to be condensed into the superfluid state. The easiest way to achieve that is to ramp the field to the BEC side of the resonance and let the gas expand in the presence of the field. If the expanded gas is elliptic, we know that the gas is Bose-Einstein condensed (we will go into more details on this in section 5.3). But this will only happen if the trap is non-isotropic in the observed plane, which is not the case. Therefore, we recompress the horizontal beam in 200 ms to a trap frequency of 5,5 kHz. Technically, it would not be necessary to recompress the horizontal beam for the momentum distribution experiments, but as it does not disturb the momentum distribution we prefer to keep the verified state as is. At the end, we switch off the trap, which takes about 5 µs. The gas expands for 0,5 ms, after which we take an absorption image. In order to reconstruct the three-dimensional distribution, we perform an inverse Abel transform as described in section 4.2. 87
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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
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: 2 ¹h = ¹ 2 a m 2 6 5 4 3 2 1 0 -1
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 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
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Ry/Rx = 2.0(1) is consistent with t
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× ��
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Bth (G) Bexp (G) 218 not seen 230 2
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Resonant scattering properties clos
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RESONANT SCATTERING PROPERTIES CLOS
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A.5 Expansion of an ultra-cold lith
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2 L. Tarruell, et al. to image the
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4 L. Tarruell, et al. of mean field
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6 L. Tarruell, et al. The starting
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8 L. Tarruell, et al. for 0.5 ms in
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10 L. Tarruell, et al. [11] M. H. A
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Appendix B Bibliography [1] H. VOGE
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[29] M. BARTENSTEIN, A. ALTMEYER, S
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[62] P. NOZIÈRES and S. SCHMITT-RI
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[98] M. MARINI, F. PISTOLESI, and G
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[131] S. STRINGARI, Collective Exci
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