Quantum Phase Transition In Arrays Of Dissipative Cavities With Two-photon Process

In recent years, the two-photon Jaynes-Cummings model has gained more and more attention due to the successful operation of two-photon maser. It has been used to study the entanglement properties, photon anti-bunching effect, squeezing effect of the atom, and quantum information transfer by many groups around the world. Further more, the manipulation of cold atom, the manufacturing of high quality optical cavity and the development of atoms and cavity field coupling technology make coupled cavity arrays attached to cold atoms become a quantum simulation platform, on which some new phenomena and effects of quantum manybody system can be implemented. Thus, the two-photon Jaynes-Cummings-Hubbard model has important significance in theory and experiment. In practice, the system inevitably interacts with the external environment, which brings in more abundant physical properties, such as the dissipation, decoherence, and entanglement of the system. Therefore, it is of great significance to study two photon Jaynes-Cummings-Hubbard model with interaction with the external environment.Coupled cavity arrays system has become a platform for quantum simulation and simulation of quantum phase transition is an important application of the system. The properties of the system are also influenced by the dissipation and detuning. Therefore, it is necessary to study the influence of dissipation and detuning on superfluid-Mott-insulator phase transition in twophoton process coupled cavity arrays.In this paper, we use the method of quasi-boson to solve the Hamiltonian of the two-photon system, then the mean field and perturbation theory are used to solve the order parameter of this two-photon system. According to the evolution of order parameter on time, we study how the dissipation and detuning influence superfluid-Mottinsulator phase transition in two-photon processes coupled cavity arrays. It is shown that, in the case of resonance, the system in the twophoton process has a larger dissipation rate than that in the one-photon process, which leads to the suppression of the long-range coherence time and enhancement of the critical hopping rate for restoring coherence. Detuning has impacts on superfluid particle number of system initial states, the time of the system maintaining a superfluid state and the critical hopping rate of restoring coherence.