Photonic analogue of Josephson effect in a dual-species optical-lattice cavity.

We extend the idea of quantum phase transitions of light in the photonic Bose-Hubbard model with interactions to two atomic species by a self-consistent mean field theory. The excitation of two-level atoms interacting with a coherent photon field is analyzed with a finite temperature dependence of the order parameters. Four ground states of the system are found, including an isolated Mott-insulator phase and three different superfluid phases. Like two weakly coupled superconductors, our proposed dual-species lattice system shows a photonic analogue of Josephson effect. i.e., the crossovers between two superfluid states. The dynamics of the proposed two species model provides a promising quantum simulator for possible quantum information processes.