Higher Order Nonclassicality from Nonlinear Coherent States for Models with Quadratic Spectrum

Anaelle Hertz,Sanjib Dey,Hichem Eleuch,Véronique Hussin

doi:10.3390/sym8050036

Abstract

Harmonic oscillator coherent states are well known to be the analogue of classical states. On the other hand, nonlinear and generalised coherent states may possess nonclassical properties. In this article, we study the nonclassical behaviour of nonlinear coherent states for generalised classes of models corresponding to the generalised ladder operators. A comparative analysis among them indicates that the models with quadratic spectrum are more nonclassical than the others. Our central result is further underpinned by the comparison of the degree of nonclassicality of squeezed states of the corresponding models.

Highlights

In 1926, Erwin Schrödinger first introduced coherent states while searching for classical like states [1]
In the very first proposal, coherent states were interpreted as nonspreading wavepackets when they move in the harmonic oscillator potential
We explore the comparative analysis of nonclassical nature of nonlinear coherent states for two different type of models associated to the nonlinear ladder operators, and realise that the models with quadratic spectrum produce higher amount of nonclassicality than the others

Summary

Introduction

In 1926, Erwin Schrödinger first introduced coherent states while searching for classical like states [1]. In the very first proposal, coherent states were interpreted as nonspreading wavepackets when they move in the harmonic oscillator potential. They minimise the Heisenberg’s uncertainty relation, with equal uncertainties in each quadrature. They are the best quantum mechanical representation of a point in phase space, or in other words, they are the closest possible quantum mechanical states whose behaviour resemble that of classical particles. Our manuscript is organised as follows: In Section 2, we discuss the general construction procedure of nonlinear coherent and squeezed states.

Nonlinear Coherent and Squeezed States

Nonclassicality via Entanglement

Nonclassical Models

Linear versus Quadratic Spectrum

Linear Plus Quadratic Spectrum

Conclusions