Vortex lattice locking in rotating two-component Bose-Einstein condensates

The vortex density of a rotating superfluid, divided by its particle mass, dictates the superfluid's angular velocity through the Feynman relation. To find how the Feynman relation applies to superfluid mixtures, we investigate a rotating two-component Bose-Einstein condensate, composed of bosons with different masses. We find that in the case of sufficiently strong interspecies attraction, the vortex lattices of the two condensates lock and rotate at the drive frequency, while the superfluids themselves rotate at two different velocities, whose ratio equals the ratio between the particle masses of the two species. In this paper, we characterize the vortex-locked state, establish its regime of stability, and find that it survives within a disk smaller than a critical radius, beyond which vortices become unbound and the two Bose-gas rings rotate together at the frequency of the external drive.