  We present the results of low lying excitation of coupled optical cavity
arrays. We derive the Dirac equation for this system and explain the existence
of Majorana fermion mode in the system. We present quite a few analytical
relations between the Rabi frequency oscillation and the atom-photon coupling
strength to achieve the different physical situation of our study and also the
condition for massless excitation in the system. We present several analytical
relations between the Dirac spinor field, order and disorder operators for our
systems. We also show that the Luttinger liquid physics is one of the intrinsic
concept in our system.
