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Table of contents
Contents
Introduction
1 Mean-eld theory of spinor Bose-Einstein Condensates
1.1 Introduction
1.2 Elements for scalar condensate
1.2.1 The ideal Bose gas
1.2.2 Bose gas with interactions
1.2.3 Calculation for scalar interacting Bose gas
1.3 Spinor BEC : Pure condensate at zero temperature
1.3.1 Hyperne structure of 23Na
1.3.2 Hamiltonian of the interacting spin-1 Bose gas
1.3.3 Mean-eld approach to the spinor Hamiltonian – HSMA
1.4 Spinor BEC : Condensate with thermal cloud at nite temperature
1.4.1 Semi-ideal HF approximation for spinor BEC
1.4.2 Simulation results for mz = 0
1.5 Conclusion
2 Experimental realization and diagnosis of spinor Bose-Einstein Condensates
2.1 Introduction
2.2 Vacuum system and experimental control
2.3 Evaporative cooling to BEC
2.3.1 Elements of evaporative cooling
2.3.2 Experimental setup of the Small-CDT
2.3.3 Two-step evaporation
2.4 Spinor condensate preparation and diagnosis
2.4.1 Magnetic eld control
2.4.2 Magnetization controlled spinor gas preparation
2.4.3 Spin diagnosis
2.5 Imaging
2.5.1 Absorption imaging
2.5.2 Imaging systems
2.5.3 Kinetics mode
2.6 Image analysis
2.6.1 Fitting
2.6.2 Counting spin populations
2.6.3 Imaging noises
2.6.4 Methods to reduce structural noise
2.7 Conclusion
3 Phase diagram of spin 1 antiferromagnetic Bose-Einstein condensates
3.1 Introduction
3.2 Experimental conguration
3.3 Experimental results and interpretation
3.4 Conclusion and perspectives
4 Collective uctuations of spin-1 antiferromagnetic Bose-Einstein condensates
4.1 Introduction
4.2 Quantum analysis of a spin-1 antiferromagnetic BEC
4.2.1 Formulation in the basis of total spin eigenstates jN; S;Mi
4.2.2 Thermal equilibrium for h ^ Szi = 0
4.2.3 Broken-symmetry approach
4.3 Generalization to arbitrary distribution of M
4.4 Hartree-Fock Approach
4.4.1 Semi-ideal Hartree Fock approximation for spinor BEC
4.4.2 Simulation results and analysis
4.5 Analysis of experimental results
4.5.1 Data analysis
4.5.2 Experimental results of temperature during evaporation
4.5.3 Experimental results of temperature during hold time
4.5.4 Fluctuation of magnetization mz at q = 0
4.6 Discussion of the results
4.7 Conclusion
Conclusion and perspectives
A Magneto-Optical Trap (MOT)
A.1 Elements of Doppler cooling and MOT
A.2 589 nm laser system
A.3 Sodium MOT
B Loading the Large Crossed Dipole Trap (Large-CDT)
B.1 Elements of optical dipole traps
B.2 Experimental setup
B.2.1 Conguration of the Large-CDT
B.2.2 Feedback system of the Large-CDT
B.3 Loading the Large Crossed Dipole Trap
B.3.1 Optimization of the MOT lasers
B.3.2 Optimization of the Large-CDT power
B.4 Compression in the Large-CDT
C Supplementary Material : Phase diagram of spin 1 antiferromagnetic Bose-Einstein condensates
C.1 Sample preparation
C.2 Stern-Gerlach expansion
C.3 Spin interaction energy
C.4 Conservation of magnetization
D Calculation details for Broken symmetry picture
D.1 Spin nematic states jN :i
D.2 Calculation of ^ in section 4.3
D.3 Fluctuation of magnetization mz at q = 0
E Published articles
Bibliography
