Superpositions of the dual family of nonlinear coherent states and their non-classical properties

TL;DR

This paper investigates superpositions of nonlinear coherent states and their duals, analyzing their non-classical properties like antibunching and squeezing, with applications to Hydrogen-like spectra and Pöschl-Teller potentials.

Contribution

It introduces two types of superpositions of nonlinear coherent states and explores their non-classical properties with specific physical system applications.

Findings

Superpositions exhibit enhanced non-classical effects.

Application to Hydrogen-like and Pöschl-Teller systems demonstrates quantum interference.

Numerical results confirm theoretical predictions.

Abstract

Nonlinear coherent states (CSs) and their {\it dual families} were introduced recently. In this paper we want to obtain their superposition and investigate their non-classical properties such as antibunching effect, quadrature squeezing and amplitude squared squeezing. For this purpose two types of superposition are considered. In the first type we neglect the normalization factors of the two components of the dual pair, superpose them and then we normalize the obtained states, while in the second type we superpose the two normalized components and then again normalize the resultant states. As a physical realization, the formalism will then be applied to a special physical system with known nonlinearity function, i.e., Hydrogen-like spectrum. We continue with the (first type of) superposition of the dual pair of Gazeau-Klauder coherent states (GKCSs) as temporally stable CSs. An application of the proposal will be given by employing the P\"oschl-Teller potential system. The numerical results are presented and discussed in detail, showing the effects of this special quantum interference.