Quantum Phase Transitions In Arrays Of Dissipative Cavities

One of the remarkable applications of coupled cavity arrays is to real-ize quantum simulators. Relying on the controllability of optical systems, it could be useful to attack some unclear physics and to explore new phe-nomenon in quantum many-body systems. In particular, over the past years the experimental progresses in engineering strong interaction of pho-tons and atoms and in fabricating large-scale arrays of high-quality cavities make this potential application may become a reality in the near future However, the quantum optical systems in general couple to an external en-vironment, which will bring the system out of equilibrium and profoundly affect the dynamics of interest. New important questions thus arise and need to be clarified, e.g. under the realistically experimental conditions, how the dissipation and decoherence would behave in these open systems.In this paper, by employing a new kind of quasi-boson approach we propose a possible answer to the above question by investigating the superfluid-Mott insulator phase transition in the array of dissipative cavi-ties. We show that the transition shares part features of the non-dissipative counterparts. There are still two quantum many-body states can be recog-nized as the delocalized and localized of photons. However, very differently, the dissipation and the decoherence give rise to a localizing effect and drive the system into mixed states. For the superfluid state, a non-equilibrium dynamical instability can lead to a sweeping to a localized state at a fi-nite time. For the Mott state, where photons are already localized at each lattice site, the localization holds but a dissipation-induced fluctuation of photon number acted on each lattice site will suppress the restoring of long-range phase coherence.