The Influences Of Detuning On The Superfluid-Insulator Phase Transition In Coupled Dissipative Cavity Arrays

Recently, the progresses of experimental techniques in trapping and cooling atoms, constructing high-quality optical microcavity, fabricating large-scale arrays of coupled cavities and engineering strong interaction of atoms and photons make coupled cavity arrays to be petential instruments, which are expected to contribute to the realization of the processing of quantum information, the inplementation of quantum computation and the quantum simulators as optical lattices does. In quantum opeics, coupled cavity arrays are used as quantum simulators of many-body physics in strongly correlated systems. A prominent example is the superfloid-insulator phase transition of polaritons in coupled QED cavity arrays as described by the Jaynes-Cummings-Hubbard model.However, in practical, as all the others quantum optical systems, experimental coupled cavity arrays are inevitably coupled to the reservior and so exposed to the dissipation, which will accumulate with time until the system break down(decoherence). In addition, the detuming will also affect the dynamics of the system, so it is necessary to figure out how this factors will affact the behaviors of the system thronghout its lifetime.In this paper, we employ a kind of quasi-bosons approah to remove the degrees of fredom of the enviroment (reservoir), carry out the effective Jaynes-Cummings-Hubbard model Hamiltonian in the presence of detuning. Then, cmbining with the single-site mean-field and perturbation theory, we figure out the superfluid order parameter of the system. By which we find that detuning from resonance allows to drive the system from the superfluid into the insulator state of the polaritons and the reverse. In addition, combining with the properties of transportation of coupled dissipative cavity arrays with detuning, we discuss the influence of detuning on the number of superfluid polaritons and the lifetime of superfuiid states. Ir suggests that the number of the superfluid polaritons will increaxe to its maximum and then reduce again along the negative part of detuning, which is similar to the spectrum of the tuansmission.