Dynamics and Ground State Properties of Two-component Bose-Einstein Condensate in Different Hyperfine States

The dynamics of the Josephson effects for a homogeneous two-component Bose-Einstein condensate in different hyperfine states is studied by two coupled nonlinear equations, which are obtained by mean field approximation. We have shown the nonlinear Josephson effects, including Plasmon and macroscopic self-trapping. We have also studied the relaxation dynamics and the system under damping will evolve into a stationary state of two equivalent components. For the equivalent two-component condensate, Green's function method is applied to find the excitation spectrum. We found that the excitation spectrum has two branched, of which one is the phonon excitation and one is of the single-particle form in the long wave-length limit. We have also studied the depletion of the condensate in the ground state.