Structure and stability of vortices in dilute Bose-Einstein condensates

Since the first realizations of Bose-Einstein condensation in dilute alkali-atom vapours in 1995, these novel quantum gases have attracted wide interest. The main focus of the research has been on finding out the coherence and superfluidity properties of the condensates. From the theoretical point of view, these systems provide a rare possibility to model an interacting many-particle system exhaustively and quantitatively accurately from first-principles quantum field theories. However, the challenge of developing a correct and computationally feasible finite-temperature formalism still remains. The coherence and superfluidity properties are intimately related to the existence and stability of quantized vortices. In this thesis, the structure and stability of vortex states in weakly interacting Bose-Einstein condensates is investigated within microscopic finite-temperature mean-field theories. An effective scheme for computationally solving the Bogoliubov-de Gennes quasiparticle eigenequations is developed, and applied to study the microscopic structure of vortex states in partially condensed vapours. In contrast to experimental observations and the predictions of the zero-temperature Bogoliubov approximation, stationary vortex states are found to be metastable within the self-consistent Popov approximation and its extensions even in the zero-temperature limit. The reasons underlying this discrepancy are analysed in detail. A criterion for the validity of stationary mean-field approximations in modelling slowly time-dependent systems is derived, and applied to precessing off-axis vortex states. Under typical experimental conditions moving vortices are shown to be deformed due to the inability of the thermal cloud to follow the vortex core rigidly. Consequently, the validity of the commonly used stationary mean-field theories in describing such states is shown to be questionable. Finally, an analysis of uniformly precessing off-axis vortex states within a fully time-dependent Popov approximation is presented. Even dynamically deformed vortices are shown to become energetically metastable as the vortex core is partially filled with noncondensed gas in the course of thermalization. This self-stabilization mechanism of vortex states, shown to occur under very general circumstances, is an inherent property of all self-consistent formalisms having a structure similar to the Popov approximation. However, it is argued to be affected by the improper treatment of the noncondensate dynamics within these formalisms, and the need for a theory taking properly into account the coupled dynamics of the condensate and the noncondensate in modelling vortex states is emphasized. The computational scheme developed is also applied to investigate possibilities to energetically stabilize multiply quantized vortex states by piercing an externally rotated condensate with a blue-detuned laser beam.reviewe