Steady-state fluorescence spectrum of a two-level atom in three-dimensional photonic crystals

In contrast to the situation in free space where the Markovian approximation and the quantum regression theorem are valid, the atom-photon interaction in photonic bandgap materials is in general nonMarkovian. In the present paper we treat the photonic crystals as background reservoirs and introduce the nonuniform noise operators caused by such nonuniform DOS distributions near the band edge. The steady state fluorescence spectrum of a two-level atom embedded in a three-dimensional photonic bandgap crystal and driven by a monochromatic classical electrical field is calculated theoretically for the first time as we known. With the help of the Liouville operator expansion, we can calculate the stationary two-time correlation functions of the atomic operators as well as the spectral distribution of the resonance fluorescence. We also use various dispersion relations to model this nonuniform DOS distribution near the bandgap. We find that if the atomic energy level is far from the bandgap, fluorescence spectra with Mollow triplets are observed.