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 proportional 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.
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