We study the quantum phase transition of light of a system when atom trapped in microcavities and interacting through the exchange of virtual photons. We predict the quantum phase transition between the photonic Coulomb blocked induce insulating phase and anisotropic exchange induced photonic superfluid phase in the system due to the existence of two Rabi frequency oscillations. The renormalization group equation shows explicitly that for this system there is no self-duality. The system also shows two Berezinskii-Kosterlitz-Thouless (BKT) transitions for the different physical situation of the system. The presence of single Rabi frequency oscillation in the system leads to the BKT transition where system shows the quantum phase transition from photonic metallic state to the Coulomb blocked induced insulating phase. For the other BKT transition when the z-component of exchange interaction is absent, the system shows the transition from the photonic metallic state to the photonic superfluid phase. We also predict the commensurate to incommensurate transition under the laser field detuning.
"Quantum phase transition of light in coupled optical cavity arrays: A renormalization group study." Adv. Theor. Math. Phys. 18 (3) 741 - 760, June 2014.