Critical onset in coherent oscillations between two weakly coupled Bose-Einstein condensates

The Josephson effects in two weakly linked Bose-Einstein condensates have been studied recently. In this letter, we study the equations derived by Giovanazzi et. al. [Phys. Rev. Lett. 84, 4521 (2000)] focusing on the effects of the initial acceleration and the velocity of the barrier on the ``dc'' current. We find that the dc current has lifetime which critically depends on the moving velocity of the barrier. Moreover, the influence of the initial acceleration is also investigated and found to be crucial for the experimental realization of the effects.