Quantum Phase Transitions In An Array Of Dissipative Cavities Each Containing Two Dipole-Coupled Atoms

In recent years, with the rapid progresses in the cold-atom physics,technology of high-precision manipulating atoms and manufacturing high-quality cavities, coupled cavity arrays become increasingly important simulation tools in quantum optics. A lot researches about quantum phase transitions have been carried out based on the coupled cavity arrays attached to ultracold atoms. These researches are usually made under the ideal conditions, neither the dissipation caused by the environment nor the dipole-dipole interaction between atoms is considered. However, the influence of external environment and dipole-dipole interaction between atoms on system are inevitable. So it is necessary to study how dissipation and dipole-dipole interaction influence the quantum phase transitions concretely.In this paper, we study the superfluid-Mott insulator quantum phase transition in a two-dimensional array of dissipative cavities each containing two dipole-coupled atoms. By employing the quasi-boson approach, unitary transformation, mean-field approximation, decoupling approximation and perturbation theory, we calculate the order parameter and draw the images of superfluid-Mott insulator quantum phase transition of the open system. We show that the dissipation caused by environment can make the system from the superfluid state into Mott insulation state. With the increase of dipole-dipole interaction between atoms, the corresponding critical time of phase transition from the superfluid state into Mott insulation state increases. And when dipole-dipole interaction is larger than a certain critical value, the system will always be in Mott insulation state.