Quantum phase transition of cold atoms in the bilayer hexagonal optical lattices

We propose a scheme to investigate the quantum phase transition of cold atoms in the bilayer hexagonal optical lattices. Using the quantum Monte Carlo method, we calculate the ground state phase diagrams which contain an antiferromagnet, a solid, a superfluid, a fully polarized state and a supersolid. We find there is a supersolid emerging in a proper parameter space, where the diagonal long range order coexists with off-diagonal long range order. We show that the bilayer optical lattices can be realized by coupling two monolayer optical lattices and give an experimental protocol to observe those novel phenomena in the real experiments.