Lasing without inversion in the V-type three-level system under the two-photon resonance condition

We investigate lasing without inversion in the closed V-type three-level system with off-resonant driving and laser fields by using both density-matrix and quantum-jump approaches. We demonstrate analytically and numerically that, under the two-photon resonance condition, it is possible to relax the severe conditions between spontaneous population decay and incoherent pump rates needed in the resonant case. We extend the same analysis to the remaining three-level systems.