By making use of a particular example of SQM, namely the array of charge qubits capacitively coupled to the resonator, we obtain a second-order phase transition between an incoherent (the high-temperature phase) and coherent (the low-temperatures phase) states of photons. This phase transition in many aspects resembles the paramagnetic-ferromagnetic phase transition. The critical temperature of the phase transition, T⋆, is determined by the energy splitting of two-level systems δ, number of qubits in the array N, and the strength of the interaction η between qubits and photons in the cavity. We obtain that the photon states manifest themselves by resonant drops in the frequency dependent transmission D(ω) of electromagnetic waves propagating through a transmission line weakly coupled to the SQM. At high temperatures the D(ω) displays a single resonant drop, and at low temperatures a peculiar \emph{double resonance response} has to be observed. The physical origin of such a resonant splitting is the quantum oscillations between two coherent states of photons of different polarizations.