Interference at quantum transitions: lasing without inversion and   resonant four-wave mixing in strong fields at Doppler-broadened transitions
  An influence of nonlinear interference processes at quantum transitions under strong resonance electromagnetic fields on absorption, amplification and refractive indices as well as on four-wave mixing processes is investigated. Doppler broadening of the coupled transitions, incoherent excitation, relaxation processes, as well as power saturation processes associated with the coupled levels are taken into account. Both closed (ground state is involved) and open (only excited states are involved) energy level configurations are considered. Common expressions are obtained which allow one to analyze the optical characteristics (including gain without inversion and enhanced refractive index at vanishing absorption) for various V, Lambda and H configurations of interfering transitions by a simple substitution of parameters. Similar expressions for resonant four-wave mixing in Raman configurations are derived too. Crucial role of Doppler broadening is shown. The theory is applied to numerical analysis of some recent and potential experiments. 
A. K. Popov