On the non-classicality features of new classes of nonlinear coherent states

In this paper, using an exponential function of intensity of radiation field, two new classes of nonlinear coherent states will be constructed. For the first class, we choose the nonlinearity function as fβ(n) = exp(βn), where β characterizes the strength of the nonlinearity of the quantum system. We show that, the corresponding β-states possess a collection of non-classicality features, only for the particular values of β and z. But, interestingly there exists finite (threshold) values of β, for which all of the non-classicality signs will disappear, in appropriate regions around the origin of the complex plane (z < |Z|). It is then illustrated that, using this threshold (or greater) value of β, the corresponding β-states behave very similar to canonical coherent states, as the most classical quantum states, in approximately whole of the space. In the continuation, we motivate to find another class of nonlinear coherent states, limited to a unit disk centered at the origin, looking like the canonical coherent states in behavior, in exactly the whole range of |z| < 1. This purpose also will be achieved by considering the nonlinearity function as fλ(n)=exp(λ/n)/n, where λ is a tunable nonlinearity parameter. The canonical coherent state's aspects of the corresponding λ-states will be refreshed, in particular cases, working with a threshold (or greater) value of λ.