  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.
