(q, ν)-deformation of generalized basic hypergeometric states

Abstract

We provide with a (q, ν)-deformation of the generalized hypergeometric coherent states defined such that the normalization function is given by generalized basic hypergeometric functions. These states are eigenstates of suitably defined deformed lowering operators. We study the domain of convergence of the corresponding normalization function. On the basis of these states, we investigate generalized basic hypergeometric Husimi distributions and corresponding phase distributions as well as new analytic basis representations of arbitrary quantum states in Bargmann and Hardy spaces. The quantum statistical properties of the states, such as photon-counting statistics and quadrature squeezing are analytically and numerically discussed in the framework of conventional quantum optics.