Spontaneous emission of a three-level lambda-type atom coupled to separate reservoirs

Considering the anisotropic dispersion model, the upper state population and spontaneous emission spectrum of three-level lambda-type atom with two transitions coupled to separate reservoirs are investigated using the resolvent operator. The upper state population reaches to a steady state value after a weak oscillation when the decay rate is zero and one transition frequency is inside the bandgap. The spectrum associated with each transition was given. Compared with results that were obtained by using isotropic dispersion model, the shape of spectrum changes significantly, and no dark line appears in the spectra.