Mitigating the phase-mismatch effect in non-resonant four-wave mixing enabled by optimal control

Phase-mismatch in nonlinear optical processes can severely limit the propagation and conversion efficiency of light fields. Here, we present an efficient optimal-control strategy to mitigate the detrimental effects of phase-mismatch in an electromagnetically induced transparency based medium via non-resonant four-wave mixing (FWM) process. By applying a set of fixed, linearly modulated coupling fields that induce a dark eigenmode, we globally optimize a single coupling detuning to minimize the spontaneous emission loss, the primary factor limiting conversion efficiency. Our approach outperforms existing FWM schemes by providing stronger robustness against large phase-mismatch variations while maintaining efficient probe-to-signal conversion. These results offer a promising route toward more efficient nonlinear frequency conversion, alleviating the stringent requirement for phase matching in experiments.