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Table of contents
Introduction
I Bose-Einstein condensates: Properties and realization
Introduction
1 Bose-Einstein condensation in harmonic traps
1.1 The BEC phase transition in ideal gases
1.2 Bose-Einstein condensation in interacting gases
1.3 The hydrodynamic approach
1.4 Dynamics of a condensate
1.5 Coherence properties of Bose-Einstein condensates
1.6 Conclusion
2 Experimental realization of a BEC
2.1 Experimental cycle: brief overview
2.2 The magnetic trap
2.3 Evaporative cooling
2.4 The imaging system
2.5 Conclusion
II 2-dimensional condensates
Introduction
3 2-dimensional Bose gases
3.1 Ideal Bose gases in 2D
3.2 Interacting gases: Condensates and quasicondensates
3.3 Phase-fluctuations and vortex-antivortex pairs: The KT-transition
4 Experimental realization of 2D condensates
4.1 The optical lattice
4.2 Selecting sites from the lattice
4.3 Experimental results
5 Detection of phase defects in 2D condensates
5.1 Interferometric detection of phase defects
5.2 Interpretation of the interference pattern
5.3 Axial imaging: Possibility for vortex detection in 2D clouds
5.4 Probability of thermal vortex configurations
5.5 Conclusion
6 Interference of 30 independent condensates
6.1 Experimental routine
6.2 Experimental results
6.3 Theoretical discussion of the results
6.4 Number squeezing and Mott-Insulator-transition
6.5 Conclusion
III Fast rotating condensates in quartic potentials
Introduction
7 Introduction to rotating condensates and the quantum Hall effect
7.1 Rotating condensates: vortices and vortex lattices
7.2 Rotating Bosons and the quantum Hall effect
7.3 Bosonic systems in the LLL
7.4 Conclusion
8 Fast rotation of a BEC in a quartic potential
8.1 Rotating bosons in anharmonic traps
8.2 Fast rotation of an ultra-cold Bose gas
9 Condensation temperature in a quadratic+quartic potential
9.1 Condensation temperature of a rotating gas in a harmonic trap
9.2 Results for the combined quadratic + quartic potential
9.3 Numerical solution for the quartic potential
9.4 Relevant results for the experimental situation
9.5 Conclusion
10 Monopole in fast rotating BECs
Conclusion
Annex
References
