Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations

TL;DR

This paper constructs Gazeau-Klauder coherent states in noncommutative spaces with minimal length uncertainty relations, demonstrating their properties and statistical behavior in both Hermitian and non-Hermitian quantum systems.

Contribution

It provides an explicit method to build coherent states in noncommutative geometries with minimal length, analyzing their uncertainty saturation and statistical properties.

Findings

Uncertainty relations are saturated for the constructed states.

Coherent wavepackets exhibit sub-Poissonian statistics.

Fractional revivals indicate superpositions of classical-like sub-wave packets.

Abstract

We provide an explicit construction for Gazeau-Klauder coherent states related to non-Hermitian Hamiltonians with discrete bounded below and nondegenerate eigenspectrum. The underlying spacetime structure is taken to be of a noncommutative type with associated uncertainty relations implying minimal lengths. The uncertainty relations for the constructed states are shown to be saturated in a Hermitian as well as a non-Hermitian setting for a perturbed harmonic oscillator. The computed value of the Mandel parameter dictates that the coherent wavepackets are assembled according to sub-Poissonian statistics. Fractional revival times, indicating the superposition of classical-like sub-wave packets are clearly identified.