Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence

The effects of incoherent pumping on the phase control of amplification without inversion (AWI) are investigated in a three-level Λ system with a weak probe field. It is shown that, similar to spontaneously generated coherence, incoherent pumping is necessary to make the system become sensitive to the relative phase. We find that the region in which AWI can be exhibited is widened with the enhancement of incoherent pumping, and that the amplitude of the probe gain can be also changed where there exists an extremum of the amplitude for a given probe detuning.