Measure of non-Gaussianity for photon-added nonlinear coherent states

Abstract

In this paper, we study the non-Gaussian character in generalized coherent states in the framework of a noncommutative space by adding photons to deformed coherent states, which is called the photon-added nonlinear coherent states (PANCSs). We find that the non-Gaussianity of PANCSs is enhanced with the increase of the photon-added number and it increases monotonically with the amplitude of the coherent states. Interestingly, we obtain that the maximal value of non-Gaussianity measure occurs at a certain critical value of the coherent state amplitude, where this critical value is determined by the kind of the deformation. Using the Mandel’s parameter, we examine the statistical properties for the PANCSs and show that the Mandel’s parameter may take positive and negative values depending on the choice of the amplitude and deformation parameter, exhibiting sub-Poissonian distribution and super-Poissonian distribution.