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

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CHAPTER 3. EXPERIMENTAL SETUP Figure 3.18: The data analysis program while performing a 2D Fermi fit. The program can show the optical density as well as absorption and reference images separately in the center of the screen. Left of the image and below integrals of a selected area are shown, with the fit superimposed. On the lower left the user can select the fitting method, and the fitting results are shown. On the very right is the selection of the images. 70
from scipy.special import erf from math import pi, sqrt from pygsl import sf 3.8. COMPUTER CONTROL isotope = p["DetectIsotop"] if isotope == 6: cgq = 1./2. # cgq is the clebsch-gordon-coefficient squared else: cgq = 7./15. pixelsize = (1./17.3/1000) # width of a pixel, in m detuning = p["Probe7PrincipalDetuning"] # laser detuning, in MHz gamma = 5.8724 # linewidth (in MHz) lamda = 670.992421e-9 # wavelength, sorry, lambda is a reserved word in python... # the scattering cross section sigma = (3*cgq*lamda**2) / (2*pi) / (1 + 4 * (detuning / gamma)**2) if fit == "Gaussian Fit": od = Hmax * Hsigma * 2 / ( # od is the optical density erf((bottom-Vmu) / (sqrt(2)*Vsigma)) - erf((top-Vmu) / (sqrt(2)*Vsigma))) * sqrt(2*pi) r["N horizontal"] = od * pixelsize**2 / sigma od = Vmax * Vsigma * 2 / ( erf((right-Hmu) / (sqrt(2)*Hsigma)) - erf((left-Hmu) / (sqrt(2)*Hsigma))) * sqrt(2*pi) r["N vertical"] = od * pixelsize**2 / sigma r["offset"] = Hoffset r["sigma horizontal / mm"] = Hsigma * pixelsize * 1000 r["sigma vertical / mm"] = Vsigma * pixelsize * 1000 r["TOF / ms"]=p["MOTImageTOF"] elif fit == "Fermi Fit": max = (Hmax + Vmax) / 2 od = 2 * pi * max * Hsigma * Vsigma r["N"] = od * pixelsize**2 / sigma r["T / TF"] = (6*sf.fermi_dirac_2(Hfermi)[0])**(-1./3.) elif fit == "Gaussian Fit 2D": od = 2 * pi * max * Hsigma * Vsigma r["N"] = od * pixelsize**2 / sigma r["aspect ratio"] = Hsigma / Vsigma r["sigma horizontal / mm"] = Hsigma * pixelsize * 1000 r["sigma vertical / mm"] = Vsigma * pixelsize * 1000 elif fit == "Fermi Fit 2D": od = 2 * pi * max * sigmax * sigmay r["N"] = od * pixelsize**2 / sigma r["T / TF"] = (6*sf.fermi_dirac_2(fermi)[0])**(-1./3.) elif fit == "Integrate": # simple summation of the optical density r["N"] = integral * pixelsize**2 / sigma r["opt. dens."] = integral Figure 3.19: The calculation of physical parameters, as it is currently used in the experiment. fit is the fitting method selected by the user, p contains the settings of the experimental parameters, r will be shown on screen. The calculations are done in a “physical” way, one can find, for example, the scattering cross section (equation (3.4)) or the temperature from equation (4.5). 71
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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
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 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: 3.8. COMPUTER CONTROL where the cod
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,-
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
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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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