Deformed photon-added nonlinear coherent states and their nonclassical properties

TL;DR

This paper introduces a general formalism for deformed photon-added nonlinear coherent states, explores their algebraic properties, potential physical realizations, and investigates their nonclassical features through specific examples like the P"oschl-Teller potential.

Contribution

It presents a new formalism for constructing deformed photon-added nonlinear coherent states and analyzes their properties, including resolution of identity and nonclassical features, with applications to physical systems.

Findings

States can be constructed for any nonlinear oscillator with known nonlinearity.

The states exhibit nonclassical properties such as squeezing and sub-Poissonian statistics.

Application to P"oschl-Teller potential demonstrates the formalism's practical relevance.

Abstract

In this paper, we will try to present a general formalism for the construction of {\it deformed photon-added nonlinear coherent states} (DPANCSs) $|\alpha, f, m>$, which in special case lead to the well-known photon-added coherent state (PACS) $|\alpha, m>$. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that, the introduced states can also be classified in the $f$-deformed coherent states, with a special nonlinearity function. Next, we will show that, these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of $m$, i.e., $|\alpha, f, -m>$, is then presented. Our approach, has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, nondegenerate spectrum. Finally, after applying the formalism to a particular physical system known as P\"oschl-Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function $f(n)=\sqrt n$, some of the nonclassical properties such as Mandel parameter, second order correlation function, in addition to first and second-order squeezing of the corresponding states will be investigated, numerically.