Control of spontaneous emission in a three-level V-type system with photonic band gap and coupled magnetic field

We study the control of spontaneous emission in a three-level V-type atom that is coupled by a static magnetic field in photonic crystals. We find that by changing the position of the upper band edge and Larmor frequency of the magnetic field, control of the steady-state behavior of spontaneous emission can be achieved. As the transition frequencies move from outside the band gap to inside, the structure of the spectral line changes from a two-peak structure to a single-peak structure, and then to a non-Lorentzian shape. With the increase of the Larmor frequency of the magnetic field, when both transition frequencies are outside the photonic band gap, the partial spectral line disappears; however, when both frequencies are inside the band gap, the non-Lorentzian shape is replaced by a Lorentzian shape. These phenomena arise from the fact that the corresponding transition frequency is pushed into or out of the band gap.