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

TL;DR

This paper introduces two new classes of nonlinear coherent states using exponential functions of radiation intensity, analyzing their non-classicality features and conditions under which they resemble classical coherent states.

Contribution

It constructs and characterizes two novel classes of nonlinear coherent states with specific nonlinearity functions and explores their transition to classical-like states based on threshold parameters.

Findings

Non-classicality features depend on parameter values.

States become classical-like beyond certain threshold parameters.

One class is limited to a unit disk, resembling canonical coherent states.

Abstract

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 f(n) = exp(\beta n), where \beta characterizes the strength of the nonlinearity of the quantum system. We show that, the corresponding \beta-states possess a collection of non-classicality features, only for the particular values of \beta and z. But, interestingly there exists finite (threshold) values of \beta, 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 \beta, the corresponding \beta-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 f(n)= exp(\lambda/n)/\sqrt{n}, where \lambda is a tunable nonlinearity parameter. The canonical coherent state's aspects of the corresponding \lambda-states will be refreshed, in particular cases, working with a threshold (or greater) value of \lambda.