is used for the diagonalization of the hamiltonian and impedance matching in terms of the polaritons. Storage and transmission of the incident field is described by the interactions between the cavities controlling the atomic transitions of the lowest lying states. Rabi splitting of vacuum induced multiphoton transitions is considered in input/output relations by the quadrature operators in the absence of the input field. Second order coherence functions are employed to investigate the photon blockade and localization-delocalization transitions of polaritons in oscillating regime of photon states described by the the population imbalance. Re fection and transmission of the single photon is investigated in the presence of the multilevel transitions resetting the bunching and antibunching of the cavity output fields.

system that inherits the networked structure of both nonlinear Josephson Junctions and harmonic oscillators is employed to describe the synchronous structures in multifrequency scheme. Emergence of dominating mode is investigated to analyze frequency locking by eigenvalue spectrum. Rabi Supersplitting and asymmetry of side peaks in power spectrum is tuned for coupled and uncoupled synchronous con?gurations in terms of frequency entrainment switched by coupling strength between resonators. Second order coherence functions are employed to investigate self-sustained oscillations in resonator mode and qubit dephasing. Snychronous structure between correlations of priviledged mode and qubit is obtained in localization-delocalization and photon blockade regime controlled by the population imbalance.