Noncommutative $q$-photon added coherent 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.