Interaction of pair coherent state with a three-level Λ-type atom and generation of a modified Bessel-Gaussian state with a vortex structure

The evolution of a system state is derived based on the nonresonant interaction of a three-level "Λ" type atom with two cavity modes at a pair coherent state and two classic fields, and a cavity field state is analysed in detail under conditional detecting. It is found that the quantized modified Bessel-Gaussian states as well as the superposition states consisting of the quantized vortex states with different weighted coefficients may be prepared through carefully preparing an initial atomic state and appropriately adjusting the interaction time. The scheme provides an additional choice to realize the two-mode quantized vortex state within the context of cavity quantum electrodynamics (QED).