Phase separation and vortex states in binary mixture of Bose-Einstein condensates in trapping potentials with displaced centers

A system of two simultaneously trapped condensates consisting of ⁸⁷Rb atoms in two different hyperfine states is investigated theoretically in the case where the minima of the trapping potentials are displaced with respect to each other. It is shown that the small shift of the minima of the trapping potentials leads to a considerable displacement of the centers of mass of the condensates, in agreement with the experiment. It is also shown that the critical angular velocities of the vortex states of the system drastically depend on the shift and the relative number of particles in the condensates, and there is a possibility to exchange the vortex states between condensates by shifting the centers of the trapping potentials.