Negative binomial states for the pseudoharmonic oscillator

Abstract

In this paper we examine some of the statistical properties of the negative binomial states (NBSs) that are a superposition of the number of states with appropriately chosen coefficients, but on the basis of Fock-vectors, which correspond to the pseudoharmonic oscillator. These states have the coherent states' behaviour not only for the harmonic limit. We examine the expectation values of the integer powers of the number operator N, which is useful when calculating Mandel's parameter for these states. Depending on the value of this parameter, we can determine the statistical behaviour of the NBSs, where these states are: sub-Poissonian, Poissonian and supra-Poissonian. Meijer's G-functions formalism was used in the calculation.