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Effective two-photon interaction in two-resonator circuit QED system

In this work we present a scheme to generate an effective two-photon interaction for a qubit coupled to two resonators in a superconducting circuit QED system where the two light modes are either from the same cavity or from two different ones, and the coupling between the two cavity modes is taken into account. It is shown that such a two-photon interaction results from a symmetry-broken potential of the superconducting circuit. We also propose applying this effective Hamiltonian, as an example, to generate the entangled states of the light fields in two resonators.