Statistics of parametrically excited photon--added coherent states

TL;DR

This paper derives explicit statistical properties, including distribution functions and phase-space representations, for photon--added coherent states affected by time-dependent oscillator frequencies, revealing how added photons influence quantum light oscillations.

Contribution

It provides explicit formulas for photon distribution, Wigner, and Q-functions of photon--added coherent states with time-dependent frequencies, advancing understanding of their nonclassical properties.

Findings

Photon distribution functions are explicitly derived.

Wigner and Q-functions are constructed explicitly.

Added photons influence oscillations of photon distribution in squeezed light.

Abstract

Photon distribution function, means and dispersions are found explicitly for the nonclassical state of light which is created from the photon--added coherent state $\vert \alpha,m \rangle$ due to a time--dependence of the frequency of the electromagnetic field oscillator. Generating function for factorial momenta is obtained. The Wigner function and Q--function are constructed explicitly for the excited photon--added coherent state of light. Influence of added photons on known oscillations of photon distribution function for squeezed light is demonstrated. oscillator are considered.