Phase control of probe response in an open ladder type system with spontaneously generated coherence

The control role of the relative phase between the probe and driving fields on the gain and dispersion in an open three-level ladder atomic system with incoherent pumping and spontaneously generated coherence is investigated. It is shown that by adjusting the value of the relative phase, the switching from lasing with inversion to lasing without inversion (LWI) can be realized; high index of the refraction with zero absorption can be achieved. It is also found that when the driving field is on resonance, the dispersion curve versus the probe detuning is very similar to the gain curve if the relative phase corresponding to the dispersion advances π/2 than that corresponding to the gain. LWI gain from the open system is obviously larger than that from corresponding closed system. When the incoherent pumping is absent, the open system can get LWI gain, moreover the gain is larger than that when the incoherent pumping presents for suitable value of the relative phase, but the corresponding closed system exhibits only absorption. In addition, manipulation effects of atomic exit and ratio of the injection rates on phase dependent gain are also analyzed.