  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.
