The Vector Soliton Solutions And Its Stability Of Two-Component Bose-Einstein Condensates

Bose-Einstein condensate is the focus of the physics in recent years, which has very important significance in theoretical and experiment study. It is a whole new state of matter and a unique system in which quantum effects manifest themselves at a macroscopic scale. In the paper, we start with the quasi one-dimensional nonlinear Schrodinger equation, and investigate the vector soliton solutions and its stability of two-component Bose-Einstein condensates trapped in an external potential. The main contents are as follow:Firstly, we introduce the basic concept of Bose-Einstein condensates and vital experiment technology of production Bose-Einstein condensate. In the mean-field approximation theory, we derive a Gross-Pitaevslii equation describing the dynamics of the Bose-Einstein condensates.Secondly, we have studied two-component Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential, using the variational approximation. We have founded three types of vector solitons:symmetric-unsplit, symmetric-split and asymmetric-unsplit solitons. The difference between the variational approximation and the numerical simulation result is extremely small. Furthermore, we test the stability of the solitons by adding strong perturbations to them.Finally, we also investigate the two-component Bose-Einstein condensates trapped in a harmonic potential. We get the analytic expression of the ground state function of condensates by using variational method. Under different interaction parameter, we compare the analytic expression of the ground state function with the numerical method, the result is very well. Further more, introducing the perturbation, we study the stability of the system by solving the excitation frequency corresponded to the Bogoliubov equation.