Control of space-dependent four-wave mixing in a four-level atomic system

We propose a scheme to demonstrate the manipulation of space-dependent four-wave mixing (FWM) in a four-level atomic system. By adjusting the detuning of the control field, one can effectively control the FWM output field transferred from a pump beam carrying orbital angular momentum. More interestingly, by appropriate choice of the intensity of the control field, the FWM field can be significantly enhanced and phase twist is almost completely suppressed. Furthermore, the superposition modes created by the interference between the FWM field and a same-frequency Gaussian beam are also discussed, showing many interesting properties. Our results may open some possibilities for phase imprinting in Bose-Einstein condensates or atom manipulation with optical tweezers.