Interaction between helical phase and Kerr nonlinear phase in vortex four- and six-wave mixing

We analyze the properties of vortex probe transmission signal (PTS), four-wave mixing (FWM) and six-wave mixing (SWM) via photonic band gap in an atomic ensemble with different topological charge ($m = 1, 2, 3$ ). We demonstrate the transfer of orbital angular momentum (OAM) from probe to SWM in experiment. We show that the shapes of vortex SWM and FWM spots intensity have been manipulated by the interaction, which can be modulated by the detuning and topological charge of related fields, between helical phase and nonlinear phase. Due to the stronger interaction, the shape of vortex FWM and SWM with m = 2, m = 3 are strongly destroyed compared to m = 1. Such results could have potential applications in logical gates for quantum computation