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

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CONTENTS into our fight agains breaking laser diodes – and helped a lot in keeping up the spirit even when everything seems to fail. The most important influence on out experiment certainly had Leticia Tarruell, my fellow graduate student. It is still unbelievable for me how many things she can do, and most of them even at the same time. Especially when this means going hiking with Christophe, it calls for admiration. How to use the experiment we learned from our predecessors, especially Thomas Bourdel and Julien Cubizolles. From them we also learned all the tricks about how to use the facilities and whom to ask for if you need something fast. I also would like to thank the postdocs who were in our lab in the very beginning of my thesis, Lev Khaykovich and Josh Milstein, as well as Servaas Kokkelmans who helped me over the first steps of Feshbach resonances when I just entered the lab. My successors as graduate students are Nir Navon and Sylvain Nascimbene. Nir has already shown his theoretical and more notably humor skills in the lab, and thus got the burden to take over the work on the computers. Sylvain has not only shown his dancing skills to us, but is already a fully skilled experimenter in the lab. The social life in our laboratory did not end at its door. Our neighbors helped a lot that we do not get depressed if the experiment is not working again. It is them who create the charming atmosphere that our laboratory has. I definitely appreciate the long discussions during lunch, especially when it was about the EU milk standards. I would also like to thank the members of my thesis comittee, Christian Miniatura, Chris Westbrook, Tilman Pfau and Roland Combescot, who have spent their summer vacation reading my thesis. The technical staff also had an important impact in our system, especially Lionel Pérenes and Patrick Giron for repairing our electronics, Didier Courtiade for various installations in our lab. Bruno, pas-Bruno and pas-pas-Bruno as well as Denis Jaggi made the walk to the stockrooms always a little excitement. Vera da Costa, Linda Krikorian and Thierry Tardieu managed the administrative work, and Nicole Neveux helped once the normal procedures would not lead to a result. Even though it is limited during thesis times, there still is a life beyond the laboratory, and so I want to thank all my friends in Paris, notably those from the Cité Universitaire, for making the time in Paris a happy stay. Without Cynthia, I would have rather gone crazy than writing a thesis, her help in supporting me during the time, but also her proofreading of the english was crucial to my success in this thesis. Thanks also to Kirk Madison, who gave me the idea and support to come to Paris. 6
Chapter 1 Introduction “The interactions of all other elements, even noble gases, is too large, therefore Helium will stay the only superfluid” writes H. Vogel in “Gerthsen-Physik” [1], a not-so-old introductory physics textbook. Nowadays it is a standard procedure in the laboratory to create superfluid dilute gases of various alkali metals. This shows how unbelievable and groundbreaking the work on cold atoms was over the last years. A superfluid is a liquid of vanishing viscosity, a situation that strange that Richard Feynman quotes John von Neuman of having it called “Dry Water” to underline how unthinkable such a state is [2]. It all started from a rather unconventional root, atomic physics, a field so unfamiliar to the general public that it is often confused with nuclear physics. It was the invention of the laser, which made this field possible. Suddenly, precision spectroscopy improved drastically and found a new use: the cooling of neutral atoms and ions. A masterpiece of this field was the invention of the magneto-optical trap, proposed by Jean Dalibard and first realized by Raab et al. [3], which made it possible to take over a hitherto independent field, the struggle to create a quantum gas and especially a Bose-Einstein condensate (BEC), attempted for decades in Hydrogen [4] but finally carried out first in 1995 with laser cooled atomic gases [5, 6]. The ado was not about nothing, as the founders of this field, Steven Chu, William D. Phillips and Claude Cohen-Tannoudji, were awarded the 1997 Nobel prize in physics. The first creators of Bose- Einstein condensation in dilute gases, Eric A. Cornell, Carl E. Wieman and Wolfgang Ketterle, followed in 2001. This enormous success led to an explosion in the field. Cold atoms are nowadays studied in many laboratories around the world. Shortly after the first realization of BEC, physicists started to ask: but what will happen with fermions? Answering this question opened a large field of 7
Page 1 and 2: École Normale Supérieure Laborato
Page 3 and 4: Contents 1 Introduction 7 2 Theory
Page 5: Acknowledgments This thesis would n
Page 9 and 10: 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
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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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ellipticity 1.6 1.4 1.2 1.0 0.8 clo
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Ellipticity 1.55 1.50 1.45 1.40 1.3
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ellipticity 1.4 1.3 1.2 1.1 1.0 0.9
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5.4. MOLECULAR CONDENSATE last sect
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density (a. u.) 70 60 50 40 30 20 1
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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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173
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