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Abstract
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By using Wigner–Heisenberg algebra (WHA) and its Fock representation, even and
odd Wigner negative binomial states (WNBSs) |M,ξ, νW±
(ν = 0 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 ν
plays an essential role in displaying highly nonclassical behaviors
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