The dark lines in the spontaneous emission spectrum of a double V-type four-level atom in double-band photonic crystal

The spontaneous emission spectrum of a double V-type four-level atom in a double-band photonic crystal is investigated. The double V-type atom is respectively coupled by the free vacuum modes and the photonic band gap modes. There are three types of dark lines in the spectrum: the first type originates from the quantum interference, the second type originates from the singularities of the density of states at the isotropic photonic band edges, and the third type originates from the quantum interference in the vacuum modes and zero density of states in the band-gap of photonic crystal. The causes leading to these three types of dark lines are investigated by varying the detuning of the atomic transitions from the band edge,by introducing smoothing parameter to eliminate the singularity of the density of states at the isotropic photonic band edges,and by introducing defect modes in the band gap of the photonic crystal.