Spontaneous emission inhibition from a driven four-level atom in a photonic band gap material

Two models (an upper levels coupling model and a lower levels coupling model) of a four-level atom embedded in a double-band photonic crystal are adopted. The effect of spontaneous emission cancellation of such systems embedded in different reservoirs are investigated. Especially, the "trapping conditions" of such systems in photonic band gap (PBG) reservoirs are discussed for the first time. We also investigate the different quantum interference effects of the lower levels coupling model embedded in an isotropic PBG reservoir. It is interesting that when the trapping conditions are fulfilled, the additional peaks, which result from the contribution of the additional singularities of Laplace transform of the delayed Green function of the isotropic PBG modes, are eliminated.