Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features

TL;DR

This paper introduces four classes of nonlinear displaced number states using algebraic and group theoretical methods, and analyzes their nonclassical properties such as sub-Poissonian statistics and Wigner functions.

Contribution

It provides a systematic algebraic and group theoretical framework for defining NDNSs, expanding their theoretical foundation beyond manual constructions.

Findings

Four classes of NDNSs are constructed using algebraic and group approaches.

The nonclassical features of NDNSs are characterized by sub-Poissonian statistics and Wigner functions.

The states exhibit nonclassical behavior confirmed through detailed analysis.

Abstract

Recently, nonlinear displaced number states (NDNSs) have been \emph{manually} introduced, in which the deformation function $f(n)$ has been artificially added to the well-known displaced number states (DNSs). In this paper, after expressing enough physical motivation of our procedure, four distinct classes of NDNSs are presented by applying algebraic and group treatments. To achieve this purpose, by considering the DNSs and recalling the nonlinear coherent states formalism, the NDNSs are logically defined through an algebraic consideration. In addition, by using a particular class of Gilmore-Perelomov-type of $SU(1,1)$ and a class of $SU(2)$ coherent states, the NDNSs are introduced via group theoretical approach. Then, in order to examine the nonclassical behaviour of these states, sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed, in detail.