Critical velocity in a binary mixture of moving Bose condensates

Abstract

We investigate the dynamic stability of two interacting Bose-Einstein condensates moving through each other with a relative velocity ${v}_{r}.$ We show that there exists a critical velocity ${v}_{r}^{(c)}$ such that for ${v}_{r}>{v}_{r}^{(c)}$ the condensate mixture becomes unstable. We construct an analytic expression of the critical relative velocity and determine the unstable collective modes. We also discuss how our results can be applied to matter-wave-mixing processes.