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

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A.2 P-wave Feshbach resonances of ultra-cold 6 Li J. ZHANG, E.G.M. VAN KEMPEN, T. BOURDEL, L. KHAYKOVICH, J. CUBIZOLLES, F. CHEVY, M. TEICHMANN, L. TARRUELL, S.J.J.M.F. KOKKELMANS, AND C. SALOMON, Physical Review A, volume 70, page 030702(R), 30 September 2004. 130
P-wave Feshbach resonances of ultracold 6 Li J. Zhang, 1,2 E. G. M. van Kempen, 3 T. Bourdel, 1 L. Khaykovich, 1,4 J. Cubizolles, 1 F. Chevy, 1 M. Teichmann, 1 L. Tarruell, 1 S. J. J. M. F. Kokkelmans, 1,3 and C. Salomon 1 1 Laboratoire Kastler-Brossel, ENS, 24 rue Lhomond, 75005 Paris, France 2 SKLQOQOD, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, People’s Republic of China 3 Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 4 Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel (Received 18 June 2004; published 30 September 2004) We report the observation of three p-wave Feshbach resonances of 6 Li atoms in the lowest hyperfine state f =1/2. The positions of the resonances are in good agreement with theory. We study the lifetime of the cloud in the vicinity of the Feshbach resonances and show that, depending on the spin states, two- or three-body mechanisms are at play. In the case of dipolar losses, we observe a nontrivial temperature dependence that is well explained by a simple model. DOI: 10.1103/PhysRevA.70.030702 PACS number(s): 34.50.�s, 03.75.Ss, 05.30.Fk, 32.80.Pj In the presence of a magnetic field, it is possible to obtain a quasidegeneracy between the relative energy of two colliding atoms and that of a weakly bound molecular state. This effect, known as a Feshbach resonance, is usually associated with the divergence of the scattering length and is the key ingredient that led to the recent observation of superfluids from fermion atom pairs of 6 Li [1–4] and 40 K [5]. Uptonow these pairs were formed in s-wave channels but it is known from condensed matter physics that fermionic superfluidity can arise through higher angular momentum pairing: p-wave Cooper pairs have been observed in 3 He [6] and d-wave cooper pairs in high-T c superconductivity [7]. Although Feshbach resonances involving p or higher partial waves have been found in cold atom systems [8–10], p-wave atom pairs have never been directly observed. In this paper we report the observation of three narrow p-wave Feshbach resonances of 6 Li in the lowest hyperfine state f =1/2. We measure the position of the resonance as well as the lifetime of the atomic sample for all combinations �f =1/2,m f�+�f =1/2,m f ��, henceforth denoted �m f ,m f ��. We show that the position of the resonances are in good agreement with theory. In the case of atoms polarized in the ground state �1/2,1/2�, the atom losses are due to threebody processes. We show that the temperature dependence of the losses at resonance cannot be described by the threshold law predicted by [11] on the basis of the symmetrization principle for identical particles. In the case of atoms polarized in �−1/2,−1/2� or that of a mixture �1/2,−1/2�, the losses are mainly due to two-body dipolar losses. These losses show a nontrivial temperature dependence that can nevertheless be understood by a simple theoretical model with only one adjustable parameter. In the �1/2,−1/2� channel, we take advantage of a sharp decrease of the two-body loss rate below the Feshbach resonance to present a first evidence for the generation of p-wave molecules. The p-wave resonances described in this paper have their origin in the same singlet �S=0� bound state that leads to the s-wave Feshbach resonances located at 543 G and �830 G. The latter has been used to generate stable molecular Bose- Einstein condensates [1–4]. In order to discuss the origin of PHYSICAL REVIEW A 70, 030702(R) (2004) RAPID COMMUNICATIONS these resonances, it is useful to introduce the molecular basis quantum numbers S,I, and l, which correspond to the total electron spin S=s 1+s 2, total nuclear spin I=i 1+i 2, and orbital angular momentum l. Furthermore, the quantum numbers must fulfill the selection rule S + I + l = even, �1� which is a result of the symmetrization requirements of the two-body wave function. Since the atomic nuclear spin quantum numbers are i1=i 2=1, and S=0, there are two possibilities for the total nuclear spin in combination with an s-wave �l=0� collision: I=0 and I=2. These two states give rise to the two aforementioned s-wave Feshbach resonances. For p-wave �l=1� collisions only I=1 is possible. This bound state may then give rise to the three p-wave Feshbach resonances of Fig. 1. This threshold state does not suffer from exchange decay, and is therefore relatively stable. Our predicted resonance field values BF (Table I) result from an analysis which takes into account the most recent experimental data available for 6 Li. The calculation has been performed for all spin channels �mf ,m�� f and a typical collision energy FIG. 1. Coupled channels calculation of p-wave binding energies, which give rise to Feshbach resonances at threshold. The twoatom states (full line) are indicated by their quantum number �m f1 ,m f2 �, while the bound state (dashed line) is labeled by the molecular quantum numbers S,I, and l. 1050-2947/2004/70(3)/030702(4)/$22.50 70 030702-1 ©2004 The American Physical Society
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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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Page 81 and 82: Chapter 5 Experimental results Well
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Page 87 and 88: 5.1. MOMENTUM DISTRIBUTION get na 3
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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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Page 115 and 116: 5.6. OTHER EXPERIMENTS AND OUTLOOK
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
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: VOLUME 93, NUMBER 5 gas. The platea
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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