Modulational Instability Of Two-Component Dipolar BECs In An Optical Lattice

Abstract The thesis is divided into two parts. The first part is a review mainly about the phenomenon of Bose-Einstein condensation (BEC), the corresponding experiment, dynamics and some important nonlinear physical phenomenon about the BEC, such as soliton, superfluid and vortex.In the second part of this paper, the modulational instability (MI) of two-Component dipolar BECs in an optical lattice is studied. The MI is a special phenomenon in the nonlinear systems. For the BEC system in optical lattice, the MI has an important influence on the creation of nonlinear localized modes, bright and dark soliton and vortex excitation and the pattern forms of the different component BEC. It has attracted wide concern for the study of the MI of the two-component BECs. Two-component BECs mean a mixture consists of two components. Compared with sigle-component BEC, it has more rich dynamic features because of the interaction between two components. The MI of the two-component BECs in an optical lattice studied years ago is examined merely on the on-site interaction. However, for the dipolar bosons in the optical lattice, the MI of these systems is affected further by site-to-site interaction, which induced by the dipole-dipole interaction. The MI for these systems has different characteristics themselves. Starting from the angle and depending on the linear stability analysis, the MI of dipolar BECs in an optical lattice is further studied.We investigated the MI regions under two situations (miscible and phase separation), and given the influence from the site-to-site interactionAs the dipole-dipole interaction can be manipulated easily, the analysis of the MI of dipolar BECs in the optical lattice can give us some useful information both for the understanding of nonlinear dynamics of BECs and for the manipulation for dipolar BECs in practice and in the quantum computation.