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

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CHAPTER 3. EXPERIMENTAL SETUP e ne rgy RF position Figure 3.13: Evaporative cooling in a dressed state picture. The solid lines on the left represent the energy levels in the magnetic trap without the RF field, while the dashed line is the dressed state energy. On the right side we consider the avoided crossing and see that the atoms, symbolized as large circles, can leave the trap if they have sufficient energy. The small circles show how the atoms may be trapped in an eggshell trap, as described in the text. A magnetic trap is a minimum of the magnetic field in free space. Atoms can be trapped in such a minimum, if they are prepared in a low field seeking state, this is a state whose energy increases with increasing magnetic field. Atoms in a high field seeking state, the other possibility, cannot be trapped as there is nothing like a magnetic field maximum in free space [89]. The situation of 6 Li is shown in figure 3.15. We can trap the atoms in the highest state. In order to remove the highest energy atoms from the trap, we drive an RF transition which transfers atoms into the untrapped lower states. As the transition depends on the magnetic field, only the atoms at a certain isomagnetic shell are removed, thus only those which are sufficiently energetic to get there. One commonly speaks of a radio frequency knife which “cuts” the high energetic tail of the atomic distribution. Another way of seeing this is to look at a dressed state picture. The radio frequency effectively shifts the lower state upwards until it crosses the upper states, as shown in figure 3.6. This creates an avoided crossing, and the atoms will be able to leave the trap once they manage to cross the magnetic field of the RF knife. One can also trap the atoms in the upper minima, symbolized by the small circles in the figure. This gives an eggshell like trap, that was proposed by Zobay and Garraway [90], and experimentally shown at Villetaneuse [91]. In the magnetic trap, we only evaporate 7 Li, as this way we are able to cool sufficiently low without loosing any of the fermions we want to work with later. Historically, we were using a sequence of linear 62
frequency / MHz 1000 950 900 850 3.6. THE COOLING STRATEGY 800 0 5 10 15 20 25 time / s Figure 3.14: The evaporation ramp. The solid line shows the linear ramps used originally, while the dashed line shows the exponential ramp used later. One should note the little linear ramp a the end of the exponential ramp to eliminated all remaining bosons. ramps for the RF knife, that were optimized independently. It turned out that by proceeding this way we converged to an approximation of an exponential function by linear pieces, as shown in figure 3.14. Thus we replaced the ramp by a simple exponential sweep which can be easily tuned as a whole. The exponential sweep is followed by a linear ramp which goes down below the hyperfine splitting in order to clear the cloud from any remaining bosons. We can improve the evaporation if we increase the scattering length by making use of the Feshbach resonance. There is a Feshbach resonance between the lowest spin states, which are not magnetically trappable. With an optical trap on the other hand, it is not easy to create a potential sufficiently deep and large as to trap the atoms directly from the MOT with good efficiency. This is why we evaporate first in the magnetic trap. 1 Once the atoms are sufficiently cold to be held in the 1 The group in Innsbruck decided to build a cavity around the vacuum chamber, 63
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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
Page 11 and 12: JILA, where they use magnetic field
Page 13 and 14: Chapter 2 Theory Da steh’ ich nun
Page 15 and 16: 2.2. A REMINDER ON SCATTERING THEOR
Page 17 and 18: 2.2. A REMINDER ON SCATTERING THEOR
Page 19 and 20: pote ntial e ne rgy or probability
Page 21 and 22: 2.3. FESHBACH RESONANCES a total an
Page 23 and 24: energy / mRy 2.0 1.5 1.0 0.5 0.0 -0
Page 25 and 26: E / GH z 0,0 -0,5 -1,0 -1,5 -2,0 0
Page 27 and 28: 2.3. FESHBACH RESONANCES relating t
Page 29 and 30: 2.3. FESHBACH RESONANCES to fit the
Page 31 and 32: second quantization, this is writte
Page 33 and 34: 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: Physics laser for the vertical. 3.6
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 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,-
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number of atoms / 1000 25 20 15 10
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5.6. OTHER EXPERIMENTS AND OUTLOOK
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Tem perature T c 0 Sarm a Ph ase 5.
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5.6. OTHER EXPERIMENTS AND OUTLOOK
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Chapter 6 Conclusions In this thesi
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Cold fermions in optical lattices c
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Appendix A Articles A.1 Experimenta
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VOLUME 93, NUMBER 5 FIG. 1. Onset o
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VOLUME 93, NUMBER 5 gas. The platea
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P-wave Feshbach resonances of ultra
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P-WAVE FESHBACH RESONANCES OF ULTRA
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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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Martin Teichmann Atomes de lithium-6 ultra froids dans la ... - TEL

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