Mott-Insulator-Superfluid Phase Transition with Coupled-Cavity Frequency Conversion System

An array of coupled cavities, each of which contains a triangle-down-level atom, is investigated. An effective Hamiltonian can be achieved under the strong classical driving. We can control the transition between Mott-insulator and superfluid states by the classical driving. The frequency conversion in one site has the same effects of nonlinear in BH hamiltonian which can induce insulator-superfluid states.