Noncommutative $q$-photon added coherent states

TL;DR

This paper constructs and analyzes noncommutative $q$-photon added coherent states, revealing enhanced nonclassical properties such as squeezing and sub-Poissonian statistics compared to ordinary harmonic oscillator states.

Contribution

It introduces a new class of photon added coherent states for a noncommutative $q$-deformed oscillator and investigates their nonclassical properties, highlighting their increased nonclassicality.

Findings

Noncommutative $q$-photon added coherent states exhibit greater quadrature squeezing.

Photon number distributions are more squeezed in the noncommutative case.

States show enhanced nonclassical features compared to standard harmonic oscillator states.

Abstract

We construct the photon added coherent states of a noncommutative harmonic oscillator associated to a $q$-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher order quadrature squeezing, namely the Hillery-type and the Hong--Mandel-type and, second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. By comparing our results with those of the usual harmonic oscillator, we notice that the quadratures and photon number distributions in noncommutative case are more squeezed for the same values of the parameters and, thus, the photon added coherent states of noncommutative harmonic oscillator may be more nonclassical in comparison to the ordinary harmonic oscillator.