The four-wave mixing (FWM) in a five-level atomic system driven by magnetic field

We present a scheme to demonstrate the manipulation of spatially dependent four-wave mixing (FWM) in a five-level atomic system controlled by an external magnetic field. The propagation of the FWM field in a five-level atomic system is investigated using a dynamic model based on the Maxwell equation, and an analytical solution for FWM is derived via the Fourier transform. Our results show a significant phase twist symmetry of the FWM field resulting from the external magnetic field, and there is no spatial phase twists or absorption at the symmetric points. Notably, in response to an external magnetic field, the peak conversion efficiency of FMW occurs at symmetrical points where the FWM phase twist direction changes symmetrically with the magnetic field. In addition, it is found that increasing vortex pump intensity or adjusting the control field power may enhance FWM conversion efficiency. Our findings have potential applications in magnetic detection and contribute to an extensive awareness of nonlinear phenomena in the atomic system.