Wigner function and the entanglement of a quantized Bessel-Gaussian vortex state of a quantized radiation field

Abstract

A new kind of quantum non-Gaussian state with a vortex structure, termed a Bessel—Gaussian vortex state, is constructed, which is an eigenstate of the sum of squared annihilation operators a2 + b2. The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality. It is also found that a quantized vortex state is always in entanglement. And a scheme for generating such quantized vortex states is proposed.