Properties Of Rotating Atomic Bose-Einstein Condensates

Bose-Einstein condensate (BEC) is the consequence of quantum statistics and is closely related to superfluid phenomena. The experimental realization of BEC in dilute alkali atom gases makes it possible that the results of theoretical and experimental studies can be compared rigorously. As being superfluid, particle current in BEC is irrotational and this makes that its respondence to rotation is different from rotating as a whole for usual fluid and is to form a vortex or vortex lattice. As a macroscopic quantum system, BEC has macroscopic wave-function. Its phase is coherent and it can exhibit special macroscopic quantum phenomena.In present dissertation, dynamical process of transition from the vortex state to the core state with lower energy and no angular excitation after removing the external rotating perturbation which makes the vortex state formed in BEC is discussed firstly. The result shows that the particle numbers in the two states oscillate with time due to the asymmetric perturbations dependent on the coordinate. For the transition induced by the asymmetric perturbations is double-direction, the particle number in the core state is always less half of the total particle number. So, from the point of view of average over time, it is a coexisting state of rotating and without rotating that is formed. This state which is in the Josephson tunneling regime of the macroscopic quantum tunneling is a quantum self-trapping state. Investigation on macroscopic quantum tunneling phenomena under the role of the rotating perturbations is made in the other part of the dissertation. By using the two-mode approximation and SU(2) coherent-state representation, the macroscopic quantum coherent tunneling and Jophson tunneling are studied in the case where the rotating frequencies of the external perturbations are fixed. It is shown that the semi-classical energy of the system has two degenerate ground states in a certain range of the parameters. The system is in the state of the superposition of the two macroscopic quantum states. Thecoherent tunnelling between them leads to the energy splitting. In another range of the parameters, the semi-classical energy of the system has only one minimum. By using the concept of off-diagonal-long-range-order, we obtain that the N-body wave-function of the system represented by the SU(2) coheren state corresponds to the order-parameter of the condensate. When the strength of the perturbation is large enough, the system is in the Josephson tunnelling regime. In the case where the rotating frequencies of the external perturbations can vary with time, a generalized nonlinear Landau-Zener equation is obtained under the mean-field approximation and it is solved numerically to study the relationship between the tunneling probability and the interactions.