| More recently, the study of the spontaneous emission of an atom in the free vacuum reservoirs has attracted considerable attention. The interests in this subject stem from many remarkable phenomena resulting from quantum interference in spontaneous emission, for example, very narrow absorption and fluorescence spectra , population trapping in a degenerate system , fluorescence quenching in the free space , phase dependent line shapes, lasing without inversion , and others. It is well known that the spontaneous emission depends not only on the properties of the excited atomic system but also on the nature of the surrounding environment which is also called reservoirs. The environment includes the types of Markov, for example, free vacuum modes (reservoirs), and non-Markov environments. Photonic band gap (PBG) material is one of Non-Markov environments. The spontaneous emission spectrum of an atom coupled to non-Markov environment is obviously to exhibit different properties compared with that coupled to Markov environment. Photonic band gap (PBG) structures have been shown to have a density of states (DOS) of emission field different from that of free-space vacuum field. The study of quantum and nonlinear optical phenomena for archetypes of atoms embedded in such PBG materials leads to the prediction of many interesting effects, for example, localization of light, photon-atom bound states, suppression and even complete cancellation of spontaneous emission, enhancement of spontaneous emission, electro-magnetically induced transparency and other phenomena.In this paper, we adopt two types of model of a three-level atom in a double-band photonic crystal described respectively by isotropic and anisotropic dispersion relations at the band edges. The one of the two models include one upper level and two lower levels. Another model includes two upper levels and one lower level. The atomic transitions from the upper levels to the lower levels are restricted to coupling by a same reservoir without lost of generality, which we assume in turns to be the isotropic PBG modes, the anisotropic PBG modes and the free vacuum modes. The calculation of spontaneous emission of the two types of model can be performed by the Laplace transform. The effects of the fine structure of the ground state levels on the spontaneous emission spectrum of an atom are studied in the first model. The quantum interferences in the three cases are analyzed and compared with each other in the second model. It is shown that new spontaneous emission lines are produced from the fine splitting of atomic ground state levels in the isotropic PBG case. The quantum interference induces additional narrow spontaneous lines near the transition from the empty upper level to the lower level. ConclusionA. Effects of splitting of lower levels on the spontaneous emission spectrum In order to investigate the effects of the splitting on the spontaneous emission spectrum in the PBG and free vacuum reservoirs, we adopt the first model as shown in Fig. 1(a). We plot the spontaneous emission spectrum as a function of detuning in the three cases as shown in Fig. 2. From the Fig. 2 (b) and (c), we see that the spontaneous emission peaks correspond to the resonant transitions from the upper level to the lower two levels. However, for the case of isotropic PBG reservoir (Fig. 2(a)), the effect of the splitting width on the spontaneous emission spectrum is quite different.In order to investigate this new feature in the isotropic PBG reservoir, we plot the spontaneous emission spectra for different splitting width as shown in Fig.3, for different widths of forbidden gap as shown in Fig.4 and different detuning of the upper level from the lower edge of the forbidden gap as shown Fig.5. From Fig. 2(a), Fig.3, Fig.4 and Fig.5, it is seen that the detuning for are unconcerned with other parameters. These additional singularities occur at,, and , and are unconcerned with other parameters. It shows conclusively that the peaks resulting from t...
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