Superposition of two nonlinear coherent states $\frac{\pi}{2}$ out of phase and their nonclassical properties

TL;DR

This paper investigates the interference effects and nonclassical properties of superpositions of two nonlinear coherent states that are $rac{ ext{ extpi}}{2}$ out of phase, applying the formalism to various physical systems and analyzing their quantum features.

Contribution

It introduces a formalism for superposing two classes of nonlinear coherent states and explores their nonclassical properties across different physical systems.

Findings

Wigner functions of superposed states exhibit negativity in phase space.

Superpositions show sub-Poissonian statistics and quadrature squeezing.

Nonclassical features are enhanced in superposed states compared to original components.

Abstract

Considering the concept of "{\it nonlinear coherent states}", we will study the interference effects by introducing the {\it "superposition of two classes of nonlinear coherent states"} which are $\frac{\pi}{2}$ out of phase. The formalism has then been applied to a few physical systems as "harmonious states", "SU(1,1) coherent states" and "the center of mass motion of trapped ion". Finally, the nonclassical properties such as sub-Poissonian statistics, quadrature squeezing, amplitude-squared squeezing and Wigner distribution function of the superposed states have been investigated, numerically. Especially, as we will observe the Wigner functions of the superposed states take negative values in phase space, while their original components do not.