Book Description

The collective excitations in a many-body system play a central role in the understanding of the system's bulk properties. Especially in quantum degenerate systems such as a Bose-Einstein condensate (BEC), studies of excitations provide a basis for interpreting complex microscopic dynamics, giving essential insight into energy flow and dissipation. Furthermore, the topological characters of excitations such as quantized vortices are of intrinsic fundamental interest. In my research, the dynamical properties of a trapped atomic BEC with an imbedded vortex lattices have been studied using mean-field quantum theory. Due to the inherent complexity of the system associated with the structure of the vortices and the density inhomogeneity, it is very difficult to solve such problems without approximations. In order to overcome such difficulties, we have approached the problem numerically using powerful parallel computational packages. This approach successfully revealed new features in the dynamics of the condensate and its vortices, features which had not been seen in any other calculation. We have also studied and proposed an approach to quantum control of quasiparticle excitations of a BEC. Motivated from these results, we extended the study of BEC dynamics to two-species spinor condensates and found interesting effects such as vortex shear flow. Results from searching for the ground state vortex configuration of an atom-molecule coupled condensate are also presented.