Phase properties of hypergeometric states and negative hypergeometric states

Abstract

We show that the three quantum states (P$\acute{o}$lya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediates states which interpolate between the binomial states and negative binomial states are essentially identical. By using the Hermitial-phase-operator formalism, the phase properties of the hypergeometric states and negative hypergeometric states are studied in detail. We find that the number of peaks of phase probability distribution is one for the hypergeometric states and $M$ for the negative hypergeometric states.