Lasing without inversion with a fluctuating pump: Gain dependence on pump noise and frequency

Recently it was reported that replacing an incoherent pumping mechanism by a spectrally colored (partially coherent) pump can lead to significant gain enhancement in lasing without inversion schemes [Phys. Rev. A 48, R4055 (1993)]. We extend that study further by considering the effects of the noise parameters (strength and bandwidth) of the pump on the gain in two types of three-level atomic energy-level schemes---the ladder and the {Λ} models. The calculations presented in this paper show a way to continuously ``tune'' the bandwidth of the pump and make a direct comparison between the gain obtained for coherent, incoherent, and partially coherent pumping. We find that for a given set of atom-field parameters, the gain for coherent pumping is larger than for incoherent pumping, and that maximum gain is obtained for a partially coherent pump. Increasing the strength of the noise also leads to an increase in the gain. The frequency of the colored pump plays a critical role in determining the maximum gain that can be obtained.