Four-wave mixing in a system

The four-wave mixing 4WM signal is calculated for a three-level quantum system in a configuration upper level 2, lower levels 1 and 3 that is driven by three fields. Pump fields E and E drive the 1-2 and 3-2 transitions, respectively. The probe field is detuned from field E by an amount . If the detuning of field E from the 1-2 transition frequency is equal to that of field E from the 3-2 transition frequency dark state pumping , there is a dark state in the absence of the probe field. Rather surprisingly, even though the probe field destroys the dark state for 0, the 4WM mixing vanishes for all in the limit of dark-state pumping. The 4WM spectra are explained within the context of a semiclassical, dressed-state picture that involves the sequential emission of a probe and signal photon.