Effects of strong driving fields in resonant four-wave mixing schemes with down-conversion

An explicit solution is obtained for the four-wave frequency mixing ω_d=ω_a-ω_b+ω_c of two strong fields a and c and two weak fields b and d in a four-level system with large Doppler broadening in collinear geometry, where the frequencies of weak fields are nearly equal, ω_b≃ω_d, and the medium is optically thin. Without weak fields there are two independent two-level systems. A pair of weak fields probes two other allowed transitions. A peak of the mixing coefficient as a function of intensity is found around an equal Rabi splitting of both two-level systems. The effect is based on a resonance between two closed cycles of four-wave mixing via different dressed states. Three, four, or six peaks are predicted in the dependence of the mixing coefficient on the frequency of the weak field; two of them are a consequence of averaging over velocities. The model allows an interpretation of the dependence of the output wave power on the intensity and detuning in recent experiments on frequency mixing in sodium vapor.