Effect of atomic initial phase difference on spontaneous emission of an atom embedded in photonic crystal

We investigate the effect of initial phase difference between the two excited states of a V-type three-level atom on its steady state behaviour of spontaneous emission. A modified density of modes is introduced to calculate the spontaneous emission spectra in photonic crystal. Spectra in free space are also shown to compare with that in photonic crystal with different relative positions of the excited levels from upper band-edge frequency. It is found that the initial phase difference plays an important role in the quantum interference property between the two decay channels. For a zero initial phase, destructive property is presented in the spectra. With the increase of initial phase difference, quantum interference between the two decay channels from upper levels to ground level turns to be constructive. Furthermore, we give an interpretation for the property of these spectra.