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The entropy squeezing properties for a two-level atom interacting with a two-mode field via two different competing transitions are investigated from a quantum information point of view. The influences of the initial state of the system and the relative coupling strength between the atom and the field on the atomic information entropy squeezing are discussed. Our results show that the squeezed direction and the frequency of the information entropy squeezing can be controlled by choosing the phase of the atom dipole and the relative competing strength of atom-field, respectively. We find that, under the same condition, no atomic variance squeezing is predicted from the HUR while optimal entropy squeezing is obtained from the EUR, so the quantum information entropy is a remarkable precision measure for the atomic squeezing in the considered system.

Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function (WDF) for a coherent or partially coherent Bessel—Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.

The pair coherent state evolution during a parametric frequency conversion is analyzed. And the wavefunction of the evolving pair coherent state in configuration space is obtained. It is found that the state may become a modified Bessel-Gaussian vortex state with topological charge index q which is a new non-Gaussian state. In coherent state representation such a modified Bessel-Gaussian vortex state is an eigenstate of sum of squared two-mode annihilation operators a2 + b2. The result obtained in this paper provides a new scheme for generating quantized vortex states in experiment with currently available technology.