Properties of multiple-component Bose-Einstein condensates

One of the most fascinating predictions of quantum statistical mechanics is that of a phase transition in a gas of identical bosons when the de Broglie wavelength exceeds the mean spacing between particles. This transition is termed Bose-Einstein condensation and the condensate that forms constitutes a macroscopic quantum mechanical object.; In this dissertation, I theoretically investigate the properties of multi-component Bose condensates and demonstrate that such condensates show surprisingly complex behavior compared to single-component condensates. The results will be crucial in understanding the physics of coupled macroscopic quantum systems.; I will first review the mean-field theory of single condensates, then generalize it to describe two-species condensates (2BECs). I will show that due to the nonlinear interspecies interactions, the ground state density distribution displays complex structures that do not exist had only one species been present. I will demonstrate the possibility of the existence of a novel metastable state of the 2BEC and the macroscopic quantum transition between a metastable and stable states. Other properties of 2BEC such as the collective elementary excitations, stability against particle number fluctuations and quantum phase diffusion will also be studied in detail.; I will then study the stability character of a condensate in vortex states. Calculations show that the stability of vortices in trapped condensates can be controlled and an unstable vortex will coherently disintegrate into new states with different angular momenta.; Finally, the investigation of spinor condensates will be presented. I will discuss the ground state spin structures and the internal spin-mixing dynamics (such as the phase-dependent population oscillation) under the nonlinear spin-exchange interactions, and how the presence of magnetic fields affects these dynamics.