The alternating-current (AC) Josephson effect is studied in a system consisting of two weakly coupled Bose Hubbard models. In the framework of the mean field theory, Gross-Pitaevskii equations show that the amplitude of the Josephson current is propo
rtional to the product of superfluid order parameters. In addition, the chemical potential--current relation for a small size system is obtained via the exact numerical computation. This allows us to propose a feasible experimental scheme to measure the Mott lobes of the quantum phase transition.
We propose a feasible scheme to realize a spin network via a coupled cavity array with the appropriate arrangement of external multi-driving lasers. It is demonstrated that the linear photon-like dispersion is achievable and this property opens up th
e possibility of realizing the pre-engineered spin network which is beneficial to quantum information processing.
