The theory of single photon scattering by a three-level atom in a dissipative coupled cavity array

A microscopic model is developed in order to analyse the effects of dissipations on single-photon transport in a coupled cavity array where one of the cavities is coupled to a three-level atom and both cavities and the three-level atom are coupled to an external environment. By employing the quasi-boson approach, the single-photon transmission and reflection amplitudes are found exactly for the Ξ -type, V-type and Λ -type three-level atoms. We focus on the dissipation properties in the case of the Λ -type system. Comparing the dissipative case with the nodissipative one, it can be found that the dissipations of the cavities and the Λ -type three-level atom significantly affect the transmission amplitude of single-photon transport. Whether the atom is in tune with the resonant frequency of the cavity or not, incomplete reflection is mostly caused by atom dissipation near the middle dip of the single-photon transport spectrum, while reduced transmission appears to be mainly controlled by cavity dissipation. Dissipations broaden the line width of the single photon transport spectrum.