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Abstract
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Following the lines of the recent papers (Ann. Phys. 362, 659670 (2015) and Mod. Phys. Lett. A
37, 1550198 (2015)), we introduce even and odd -deformed binomial states (-deformed BSs) |M, , ±,
in which for = 0, they lead to ordinary even and odd binomial states (BSs). We show that these states
reduce to the -deformed cat-states in the special limits. We establish the resolution of identity property
for them through a positive definite measure on the unit disc. The effect of the deformation parameter
on the nonclassical properties of introduced states is investigated numerically. In particular, through the
study of squeezing, we show that in contrast with the odd BSs, the odd -deformed BSs have squeezing.
Also, we show that the even and odd -deformed BSs minimize the uncertainty relation for large values
of .
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