Dynamics of two-component Bose-Einstein condensates coupled with the environment

We investigate the dynamics of an open Bose-Einstein condensate system consisting of two hyperfine states of the same atomic species which are coupled by a tunable Raman laser. It has already been suggested that the detuning between the laser frequency and transition frequency affect significantly the dynamics of the pure condensate. Here we show that the detuning effect is suppressed by noise and dissipation caused by the environment. The increase of coherence and purity are also displayed for specific parameters. As a verification of the lowest order approximation we derive the hierarchy of motion equations in the second-order approximation. It turns out that the former one can describe the dynamical evolution qualitatively for weak noise and dissipation and quantitatively for strong noise and dissipation.