Phase control of inversionless gain in a closed atomic system with Doppler broadening

We studied the controlling role played by the relative phase between the probe and driving fields on inversionless gain of the probe field in a closed and Doppler broadened Λ-type three-level system with spontaneously generated coherence (SGC). It was found that(1) Regardless of the driving field being in or off resonance, and regardless of the probe and driving fields being co- or counter- propagating, the gain maximum value always varies periodically with variation of the relative phase with the period 2π. (2) When the driving field is in resonance, the gain maximum value decreases monotonicly with Doppler width increasing, and moreover, the decreasing in the counter-propagation case is faster than that in the co-propagation case. When the driving field is off resonance, the gain maximum value does not monotonicly decrease or increase with Doppler width increasing. In both above cases, the largest inversionless gain can be gotten by adjusting the relative phase. (3) The contribution of SGC to the inversionless gain is much larger than that of the dynamically induced coherence.