Laser without inversion in a Δ-configuration three-level system with cyclic transition

In the case of incoherent pumping, laser without population inversion in a resonant three-level Delta-configuration system is investigated. By taking the strong coupling field limit, we obtain the approximate steady-state analytical solution of populations and imaginary part of coherences within the dressed-state regime, and discuss the condition of the generating of laser without inversion and the dependences of population distribution and system gain on Rabi frequency of the probe and coherence fields. The results show that the resonant three-level Delta-configuration system is always in the state of no population inversion, and laser without inversion occurs if one of the two fields is strong. When one of the two fields is much stronger than the other one, the gain without inversion is independent of the two Rabi frequencies.