Eliminating nonlinear phase mismatch in resonantly enhanced four-wave mixing

Resonantly enhanced four-wave mixing in double-Λ systems is limited by ac-Stark induced nonlinear phase shifts. With counter-propagating pump fields the intensity-phase coupling has minimal impact on the dynamics, but it is of critical importance for co-propagation. The nonlinear phase terms lead to an increase of the conversion length linearly proportional to the inverse seed intensity, while without nonlinear phase-mismatch the scaling is only logarithmic. We here show that the ac-Stark contributions can be eliminated while retaining the four-wave mixing contribution by choosing a suitable five-level system with appropriate detunings.