Double-layer Bose-Einstein condensates with a large number of vortices

In this paper we systematically study the double-layer vortex lattice model, which is proposed to illustrate the interplay between the physics of a fast rotating Bose-Einstein condensate and the macroscopic quantum tunneling. The phase diagram of the system is obtained. We find that under certain conditions the system will exhibit a phase transition which is a consequence of the competition between interlayer coherent hopping and the interlayer density-density interaction. In one phase the vortices in one layer coincide with those in the other layer. In another phase two sets of vortex lattices are staggered, and as a result the quantum tunneling between two layers is suppressed. To obtain the phase diagram we use the quantum Hall mean field and Thomas-Fermi mean field theories. Two different criteria for the transition taking place are obtained, which reveals some fundamental differences between these two mean-field states. The sliding mode excitation is also discussed.