Non-Markovian dynamic evolution of spontaneous emission decay of a two-level atom embedded in one-dimensional photonic crystals

The dynamic evolution of atomic spontaneous emission in one-dimensional photonic crystals (1DPC) is investigated by using mode functions for the 1DPC. Our attention is focused on the non-Markovian processes in the first several optical cycles of the spontaneous emission decay. The integral-differential dynamic equation is directly solved by numerical calculation without using the Markovian approximation. The interference of the multireflected fields plays an important role in the non-Markovian processes. Due to the interference of the fields successive arrived at the atom due to the reflection at the interfaces, the decay rate shows a series of pulselike peaks. If the interference is constructive, the spontaneous decay is enhanced, while if the interference is destructive, the spontaneous decay is suppressed. The steady decay rate is approximately equal to the vacuum decay rate, when the atomic transition frequency corresponds to an allowed normal mode of the 1DPC. The spontaneous emission decay is suppressed if the atomic transition frequency is within the forbidden gap of the 1DPC.