Abstract
By using Wigner–Heisenberg algebra (WHA) and its Fock representation, even and odd Wigner negative binomial states (WNBSs) [Formula: see text] ([Formula: see text] corresponds to the ordinary even and odd negative binomial states (NBSs)) are introduced. These states can be reduced to the Wigner cat states in special limit. We establish the resolution of identity property for them through a positive definite measure on the unit disc. Some of their nonclassical properties, such as Mandel’s parameter and quadrature squeezing have been investigated numerically. We show that in contrast with the even NBSs, even WNBSs may exhibit sub-Poissonian statistics. Also squeezing in the field quadratures appears for both even and odd WNBSs. It is found that the deformation parameter [Formula: see text] plays an essential role in displaying highly nonclassical behaviors.
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