Even and odd $\lambda$ λ -deformed binomial states: minimum uncertainty states

Abstract

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 $\lambda$ -deformed binomial states ( $\lambda$ -deformed BSs) $ \vert M,\eta,\lambda\rangle_{\pm}$ , in which for $\lambda =0$ , they lead to ordinary even and odd binomial states (BSs). We show that these states reduce to the $\lambda$ -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 $\lambda$ 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 $\lambda$ -deformed BSs have squeezing. Also, we show that the even and odd $\lambda$ -deformed BSs minimize the uncertainty relation for large values of $\lambda$ .