Phase modulation of transient evolution of atomic response in open lambda-type system with spontaneously generated coherence

We study the effects of the relative phase, Φ, between the probe and driving fields on the transient evolution of the atomic response from different respects in an open lambda-type system with spontaneously generated coherence. We find that: variation of value of Φ will obviously change the transient evolution process, transient and stationary values of gain, absorption and dispersion but has no any effect on the transient evolution of populations. For the same value of Φ, the stationary gain without inversion (GWI) when the incoherent pumping exists is much larger than that when the incoherent pumping is absent, the time needed to reach at the stationary state when the incoherent pumping exists is much shorter than that when the incoherent pumping is absent. The initial condition varying has remarkable effects on the phase-dependent transient evolution process, transient value of GWI but doesn’t vary size of stationary value of GWI. Varying the ratio C of the atomic injection rates and exit rate γ₀ has evident effects on the phase-dependent transient evolution process, transient and stationary values of GWI. Our study result shows that the transient evolution of the atomic response in the open system presents some considerable difference from that in the corresponding closed system, specially in the open system we can get much larger GWI than that in the corresponding closed system. In addition, we give a brief discussion about effects of the relative phase on the transient evolution of the atomic response in the open system without SGC, and obtain some results much different from those obtained in the open system with SGC.