Negative binomial states of a single field mode are introduced and their properties are compared with those of the (positive) binomial states. We find that the two types of state have similar properties if the roles of the creation and annihilation operators are interchanged.
We introduce excited binomial states and excited negative binomial states of the radiation field by repeated application of the photon creation operator on binomial states and negative binomial states. They reduce to Fock states and excited coherent states in certain limits and can be viewed as intermediate states between Fock states and coherent states. We find that both the excited binomial states and excited negative binomial states can be exactly normalized in terms of hypergeometric functions. Base on this interesting character, some of the statistical properties are discussed.
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schrodinger cat states in a certain limit.The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras.It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.``
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schrödinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.