Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials

TL;DR

This paper explores the unique quantum and classical behaviors of coherent states linked to exceptional orthogonal polynomials in extended harmonic oscillators, revealing how different ladder operators influence state dynamics.

Contribution

It introduces new coherent states for systems with exceptional orthogonal polynomials and compares their quantum-classical behavior based on different ladder operators.

Findings

Coherent states of the annihilation operator show quantum behavior.

Linearised coherent states exhibit wavepacket oscillations and collisions.

Interference fringes indicate quantum phenomena amidst classical-like evolution.

Abstract

We construct the coherent states and Schr\"odinger cat states associated with new types of ladder operators for a particular case of a rationally extended harmonic oscillator involving type III Hermite exceptional orthogonal polynomials. In addition to the coherent states of the annihilation operator, $c$, we form the linearised version, \tilde{c}, and obtain its coherent states. We find that while the coherent states defined as eigenvectors of the annihilation operator $c$ display only quantum behaviour, those of the linearised version, \tilde{c}, have position probability densities displaying distinct wavepackets oscillating and colliding in the potential. The collisions are certainly quantum, as interference fringes are produced, but the remaining evolution indicates a classical analogue.