Optical Polariton Transistor based on the virtual photon blockade in circuit QED

We consider the single photon transistor in coupled cavity system of resonators interacting with multilevel superconducting artificial atom simultaneously. Effective single mode transformation 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.