Bose-Einstein condensation in atomic alkali gases

This thesis presents an analysis of Bose-Einstein condensed, magnetically trapped, weakly-interacting, atomic alkali gases. The time-independent Gross-Pitaevskii, Bogoliubov, and finite-temperature Hartree-Fock-Bogoliubov mean-field formalisms are used. In order to place this work in a general scientific context, the historical and theoretical backgrounds to the phenomenon of Bose-Einstein condensation are summarized. The experimental techniques which lead to its laboratory observation in dilute alkali gases will also be briefly discussed. These techniques have led to the production of ultra-cold gases. Such gases have properties that are significantly different from those encountered in Bose-Einstein condensed helium super-fluids.;Starting with zero-temperature models, a systematic analysis of dilute, inhomogeneous condensates is presented. Consideration is given to condensates with both effectively attractive and repulsive interactions. The condensate density, aspect ratio, and loss rates are modeled using the Gross-Pitaevskii equation. Extensive comparison is made with the Thomas-Fermi and variational approximations that are used in the literature to study condensed gases. Numerical calculations of the Bogoliubov quasi-particle excitations, which are equivalent to the condensate normal-modes, are compared with the experimentally measured, low-temperature condensate excitations. The possible existence of vortex state condensates is also considered.;The finite-temperature properties of trapped systems are examined using both the Popov approximation of the Hartree-Fock-Bogoliubov theory, and a simple "two-gas" model. Specific, quantitative comparisons are made with published results for finite-temperature excitations. Qualitative comparisons are made between the results of the Popov approximation, two-gas model, and other published models for condensate fraction and thermal density distribution.;The coherence properties of trapped systems are examined by application of standard optical techniques to treat matter-wave fields. Expressions for the equal-time, two- and three-particle coherence functions are derived within the mean-field framework. The spatial and temperature dependence of these functions is examined in the zero-separation limit.