Time evolution of the relative phase in two-component Bose-Einstein condensates with a coupling drive

The dynamics of two-component Bose-Einstein condensates with coupling drive is studied using a pair of bosonic operators. We demonstrate that the effect of the coupling drive on the evolution of the relative phase of the two-component Bose-Einstein condensates depends on the initial relative phase difference between the two condensates. In some special initial phase differences $(\ensuremath{\varphi}=0$ and $\ensuremath{\pi})$ the condensate density are not sinusoidal functions of time, and the interference pattern is not steady either. The coupling drive also reduces the amplitude and the period of the oscillation. Our theoretical result confirms the experimental observations reported in Phys. Rev. Lett. 81, 1543 (1998).