Even and odd generalized hypergeometric coherent states

TL;DR

This paper explores a broad class of generalized hypergeometric coherent states, including their even and odd variants, analyzing their mathematical properties, photon statistics, and quantum optical features using Mellin transform techniques.

Contribution

It introduces and analyzes even and odd generalized hypergeometric states, providing solutions to the moment problem and examining their quantum optical properties.

Findings

Photon-counting statistics characterized for specific parameters

Quantum optical properties analyzed of the states

Geometry of the states discussed

Abstract

In this paper, we investigate a large class of generalized hypergeometric states $|p,q,z\rangle$, depending on a complex variable $z$ and two sets of parameters, $(a_1,\cdots,a_p)$ and $(b_1,\cdots,b_q)$. Even and odd generalized hypergeometric states $|p,q,z\rangle_e$ and $|p,q,z\rangle_o$ are also defined and analyzed. The moment problem is solved by the Mellin transform techniques. For particular values of $p$ and $q$, the photon-counting statistics, quantum optical properties and geometry of these states are discussed.