Modulation of atomic exit and injection rates on the phase-dependent gain without inversion in a Doppler broadened open four-level system

It is shown that in a Doppler broadened open N-type four-level atomic system with spontaneously generated coherence (SGC), the gain without inversion (GWI) is very sensitive to the variation of the relative phase between the probe field and the driving field; the atomic exit rate (R-0) and the ratio (S) of the atomic injection rates have a considerable modulation effect on the phase-dependent GWI. GWI first increases and then decreases with R-0 increasing; in a certain value range of S, GWI increases monotonically with S increasing; by adjusting the values of R-0 and S, in an open system a much larger GWI can be obtained than in the corresponding closed system [2011 Phys. Rev. A 83 043805]. The modulation effects of R-0 and S on the phase-dependent GWI in the case with the counter-propagating probe and driving fields are stronger than those in the co-propagating case, GWI in the co-propagating case is much larger than that in the counter-propagating case.