Truncated generalized coherent states

TL;DR

This paper introduces a broad class of generalized coherent states for quantum harmonic oscillators, exploring their statistical properties and non-classical behaviors, including sub- and super-Poissonian statistics, with specific cases like Wright and Mittag-Leffler states.

Contribution

It develops a new framework for generalized coherent states with diverse statistical properties, extending beyond canonical states and analyzing their non-classical features.

Findings

Generalized coherent states exhibit non-Poissonian excitation distributions.

States show sub-Poissonian or super-Poissonian statistics depending on parameters.

Specific cases like Wright states display unique non-classical properties.

Abstract

A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight function. Relying on this approach, in the present scenario coherent states are generalized over the canonical or finite dimensional Fock space of the harmonic oscillator. A class of generalized coherent states is determined such that the distribution of the number of excitations departs from the Poisson statistics according to combinations of stretched exponential decays, power laws and logarithmic forms. The analysis of the Mandel parameter shows that these generalized coherent states exhibit (non-classical) sub-Poissonian or super-Poissonian statistics of the number of excitations for small values of the label, according to determined properties. The statistics is uniquely sub-Poissonian for large values of the label. As particular cases, truncated Wright generalized coherent states exhibit uniquely non-classical properties, differently from the truncated Mittag-Leffler generalized coherent states.