# Generalized photon-added associated hypergeometric coherent states: characterization and relevant properties

## TL;DR

This paper introduces a new class of generalized photon-added coherent states linked to associated hypergeometric functions, thoroughly analyzing their mathematical properties and quantum optical characteristics, including sub-Poissonian photon statistics.

## Contribution

The paper constructs and characterizes a novel set of photon-added coherent states related to associated hypergeometric functions, extending previous work and providing explicit solutions for the moment problem.

## Key findings

- States satisfy all required mathematical and physical properties
- Explicit solution of the Stieltjes power-moment problem using Meijer's G-function
- States exhibit sub-Poissonian photon number statistics

## Abstract

This paper presents the construction of a new set of generalized photon-added coherent states related to associated hypergeometric functions introduced in our previous work (Hounkonnou M N and Sodoga K, 2005, J. Phys. A: Math. Gen 38, 7851). These states satisfy all required mathematical and physical properties. The associated Stieltjes power-moment problem is explicitly solved by using Meijer's G-function and the Mellin inversion theorem. Relevant quantum optical and thermal characteristics are investigated. The formalism is applied to particular cases of the associated Hermite, Laguerre, Jacobi polynomials and hypergeometric functions. Their corresponding states exhibit sub-Poissonian photon number statistics.