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Table of contents
1. Introduction
2. Elements of Bose-Einstein condensation
2.1. The scalar Bose-Einstein condensate in a 3d harmonic trap
2.1.1. The ideal Bose gas
2.1.2. The role of interactions
2.1.3. The mean-field approximation at T = 0
2.1.4. Mean field approximation at T > 0
2.2. The scalar Bose gas in a 1D harmonic trap
2.2.1. Bose gases in one dimension
2.2.2. Quasicondensation in 3D anisotropic trap
2.2.3. Phase Fluctuations in TOF
2.3. The spin-1 Bose Gas
2.3.1. Hyperfine structure of Na atoms
2.3.2. Two-body scattering between Na atoms
2.3.3. The Zeeman shift
2.3.4. The Spinor Many-body Hamiltonian
2.3.5. Spinor BEC in the single spatial mode
3. Production and characterization of a spin-1 Bose-Einstein condensate of Sodium atoms
3.1. Experimental Setup and cooling techniques
3.1.1. UHV chamber and atomic source
3.1.2. Magneto-optical trap
3.1.3. The crossed dipole trap and the dimple optical traps
3.1.4. Stern-Gerlach time of flight
3.1.5. Imaging after TOF
3.2. Manipulating internal states with spin degrees of freedom
3.2.1. Magnetic field control
3.2.2. Rabi Oscillations
3.2.3. Adiabatic rapid passage
3.2.4. Magnetization preparation
3.3. Image characterisation
3.3.1. Magnification characterisation
3.3.2. Calibration of spin-dependent cross sections
3.4. Image analysis
3.4.1. Noise modelisation
3.4.2. Noise reduction
3.5. From the 3d to the 1d geometry
3.5.1. The adiabatic transfer
3.5.2. Characterisation of the trap frequencies
4. Stepwise Bose-Einstein Condensation in a Spinor Gas
4.1. Article
4.2. Supplementary Materials
4.2.1. Experimental sequence
4.2.2. Evaporation dynamics
4.2.3. Extracting Tc
4.2.4. Theoretical models of spinor gases at finite temperatures .
5. Spin-1 BEC in 1D: Spin domains and phase transition
5.1. Stable phases of a 1D Spin-1 antiferromagnetic BEC
5.1.1. The uniform case
5.1.2. Adding an harmonic potential in the LDA approximation
5.1.3. The phase transition
5.1.4. GP simulation vs LDA solution
5.2. 1D-3D crossover
5.3. Preparation and study of spin domains
5.3.1. Minimisation of magnetic field gradients
5.3.2. Fitting the Spin Domains
5.3.3. Equation of State and temperature
5.4. 1D Transition
6. Binary mixtures
6.1. Spin-dipole polarisability
6.1.1. Polarised cloud response: z0
6.1.2. Spin-dipole polarisability vs magnetisation
7. Conclusions and perspectives
Appendices
A. Adiabatic Transfer of a quasi-condensate in 1D
A.1. Theory of quasi-condensate
A.2. The adiabatic transfer
B. Numerical solution of the spin 1 Gross-Pitaevskii equations
