Statistical properties and algebraic characteristics of quantum superpositions of negative binomial states

We introduce new kinds of states of quantized radiation fields, which are t he superpositions of negative binomial states. They exhibit remarkable nonc lassical properties and reduce to Schrodinger cat states in a certain limit . The algebras involved in the even and odd negative binomial states turn o ut 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.