Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping

This paper theoretically studies the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms in hybrid structures. We provide several approaches correspondingly based on the mean field method and spin wave theory. In the present paper, we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weak-coupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.