The Mth nonlinear coherent states

Abstract

Since radiation field states are very important in the interaction with the various atomic structures, in this article we introduce a new type of quantum states, which we call ‘Mth nonlinear coherent states’. We define these states based on acting of the number operator M times nˆM on a nonlinear coherent state. By analyzing the photon distribution function and its overlap with the nonlinear coherent states, it becomes clear that these states are very similar to the corresponding nonlinear coherent states. We also investigate the nonclassical features of such states for different values of M, and it is determined that the occurrence of sub-Poissonian photon statistics, normal squeezing, and amplitude squared squeezing are considerable nonclassical properties of the Mth nonlinear coherent states. Also, examining the Husimi function shows a local behavior for the introduced states. Furthermore, by calculating the Wigner function, we find out that in some points of the phase space, the value of this function is negative which could be considered as a nonclassical feature for these states.