Spontaneous emission from a three-level atom placed in three-dimensional photonic crystals in the long-time limit

The paper describes the spontaneous emission from a three-level atom placed in a periodic dielectric microstructure which exhibits a complete three-dimensional photonic band gap. By using the Euler approach, the upper level population of the atom is calculated for a wide range of relationships between the Rabi frequency and the detuning of the atomic transition frequency from the upper band edge. The results indicate that there are three cases of the relationship between Rabi frequency and detuning, which determine distinctive states of the atomic population in the long-time limit. When the detuning is greater than the Rabi frequency, the upper level has a zero steady-state atomic population, which leads to enhancement of spontaneous emission. When the magnitude of the detuning is less than the Rabi frequency, the upper level has a nonzero steady-state atomic population, which leads to suppression of spontaneous emission. When the negative detuning is greater than the Rabi frequency, the upper level has a nondecaying oscillatory-state atomic population due to long-time atomic splitting. These three properties of the spontaneous emission are relevant to several optical devices on an atomic scale, such as optical memories, switches and clocks.