Photonic phase transition in circuit quantum electrodynamics lattices coupled to superconducting phase qubits

A hybrid quantum architecture was proposed to engineer a localization-delocalization phase transition of light in a two-dimension square lattices of superconducting coplanar waveguide resonators, which are interconnected by current-biased Josephson junction phase qubits. We find that the competition between the on-site repulsion and the nonlocal photonic hopping leads to the Mott insulator-superfluid transition. By using the mean-field approach and the quantum master equation, the phase boundary between these two different phases could be obtained when the dissipative effects of superconducting resonators and phase qubit are considered. The good tunability of the effective on-site repulsion and photon-hopping strengths enable quantum simulation on condensed matter physics and many-body models using such a superconducting resonator lattice system. The experimental feasibility is discussed using the currently available technology in the circuit QED.