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 L. Tarruell 1 , M. Teichmann 1 , J. McKeever 1 , T. Bourdel 1 , J. Cubizolles 1 , L. Khaykovich 2 , J. Zhang 3 , N. Navon 1 , F. Chevy 1 , and C. Salomon 1 1Laboratoire Kastler Brossel, École normale supérieure, 24, rue Lhomond, 75005 Paris, France 2Department of Physics, Bar Ilan University, 52900 Ramat Gan, Israel 3SKLQOQOD, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, P. R. China Summary. — We present an experimental study of the time of flight properties of a gas of ultra-cold fermions in the BEC-BCS crossover. Since interactions can be tuned by changing the value of the magnetic field, we are able to probe both non interacting and strongly interacting behaviors. These measurements allow us to characterize the momentum distribution of the system as well as its equation of state. We also demonstrate the breakdown of superfluid hydrodynamics in the weakly attractive region of the phase diagram, probably caused by pair breaking taking place during the expansion. 1. – Introduction Feshbach resonances in ultra cold atomic gases offer the unique possibility of tuning interactions between particles, thus allowing one to study both strongly and weakly interacting many-body systems with the same experimental apparatus. A recent major achievement was the experimental exploration of the BEC-BCS crossover [1, 2, 3, 4, 5, 6], a scenario proposed initially by Eagles, Leggett, Nozières and Schmitt-Rink to bridge the gap between the Bardeen-Cooper-Schrieffer (BCS) mechanism for superconductivity in metals, and the Bose-Einstein condensation of strongly bound pairs [7, 8, 9]. Here, we present a study of the crossover using time of flight measurements. This technique gives access to a wide range of physical properties of the system and has been successfully used in different fields of physics. The observation of elliptic flows was for instance used to demonstrate the existence of quark-gluon plasmas in heavy ion collisions [10]. In cold atoms, the ellipticity inversion after free flight is a signature of Bose-Einstein condensation [11, 12]. In an optical lattice the occurrence of interference peaks can be used as the signature of the superfluid to insulator transition [13] and, with fermions, it can be used c○ Società Italiana di Fisica 1
2 L. Tarruell, et al. to image the Fermi surface [14]. Two series of time-of-flight measurements are presented: expansion of the gas without interactions, which gives access to the momentum distribution, a fundamental element in the BEC-BCS crossover, or with interactions, which allows us to characterize the equation of state of the system, and probe the validity of superfluid hydrodynamics. 2. – Experimental method In a magnetic trap, a spin polarized gas of N = 10 6 6 Li atoms in |F = 3/2, mF = +3/2〉 is sympathetically cooled by collisions with 7 Li in |F = 2, mF = +2〉 to a temperature of 10 µK. This corresponds to a degeneracy of T/TF ∼ 1, where TF = �¯ω(6N) 1/3 /kB is the Fermi temperature of the gas. The magnetic trap frequencies are 4.3 kHz (76 Hz) in the radial (axial) direction, and ¯ω = (ωxωyωz) 1/3 is the mean frequency of the trap. Since there are no thermalizing collisions between the atoms in a polarized Fermi gas, the transfer into our final crossed dipole trap, which has a very different geometry (Fig. 1), is done in two steps. We first transfer the atoms into a mode-matched horizontal single beam Yb:YAG dipole trap, with a waist of ∼ 23 µm. At maximum optical power (2.8 W), the trap depth is ∼ 143 µK (15 TF ), and the trap oscillation frequencies are 6.2(1) kHz (63(1) Hz) in the radial (axial) direction. The atoms are transferred in their absolute ground state |F = 1/2, mF = +1/2〉 by an RF pulse. We then sweep the magnetic field to 273 G and drive a Zeeman transition between |F = 1/2, mF = +1/2〉 and |F = 1/2, mF = −1/2〉 to prepare a balanced mixture of the two states (better than 5%). At this magnetic field, the scattering length between both states is −280 a0 (Fig. 2). After 100 ms the mixture has lost its coherence, initiating collisions in the gas. During the thermalization process about half of the atoms are lost. We then perform a final evaporative cooling stage by lowering the trap depth to ∼ 36 µK. At this point, we ramp up a vertical Nd:YAG laser beam (power 126 mW and waist ∼ 25 µm), obtaining our final crossed dipole trap configuration (Fig. 1). The measured degeneracy is T/TF � 0.15. The magnetic field is then increased to 828 G (in the vicinity of the Feshbach resonance, see Fig. 2), where we let the gas thermalize for 200 ms before performing subsequent experiments. 3. – Momentum distribution In standard BCS theory, the ground state of an homogeneous system is described by a pair condensate characterized by the many-body wave function |ψ〉 = � (uk + vka † k k,↑ a† −k,↓ )|0〉, where |0〉 is the vacuum and a † k,σ is the creation operator of a fermion with momentum k and spin σ. In this expression, |vk| 2 can be interpreted as the occupation probability in momentum space, and is displayed in Fig. 3a for several values of the interaction
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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
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° 0.67 0.66 0.65 0.64 0.63 0.62 0.
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Page 111 and 112: E / GH z 0 -1 -2 |1,1〉 ⊗ |1/2,-
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Page 117 and 118: Tem perature T c 0 Sarm a Ph ase 5.
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Page 121 and 122: Chapter 6 Conclusions In this thesi
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Page 125 and 126: Appendix A Articles A.1 Experimenta
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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: A.5 Expansion of an ultra-cold lith
Page 155 and 156: 4 L. Tarruell, et al. of mean field
Page 157 and 158: 6 L. Tarruell, et al. The starting
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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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