Superfluid-Insulator Transition Of The Dipolar Bosons In An Optical Lattice

This thesis is divided into two parts. The first part is a review main about the condition of Bose-Einstein condensation realization,the corresponding experiment,Gross-Pitaevskii equation (GP equation) and some important physical phenomenon about the BEC. In the second part of this paper, the modulational instability of dipole Bose-Einstein Condensates (BEC) in an optical lattice is studied. The modulational instability is a special phenomenon in the nonlinear systems. For the system of ordinary BEC in optical lattice, the modulational instability has important influence on the superflui-Mott insulator transition, bright and dark soliton excitation and the pattern forms of the different component BEC. In the ordinary BEC system, the modulational instability comes from the on-site interaction. But for the dipolar bosons in the optical lattice, the dipole-dipole interaction can induce site to site interaction , the modulational instability for these systems have different characteristics themselves. Basis on the linear stability analysis, the modulational instability of dipole Bose-Einstein Condensates (BEC) in an optical lattice is studied. As the dipole-dipole interaction can be manipulate easily, the analysis of the modulational instability of dipole BEC in the optical lattice can give us some useful information both for the understanding nonlinear dynamics of BEC and for the how to manipulate dipole BEC in practice and in the quantum computation.