In this paper, we introduce two new classes of nonlinear squeezed states that we name as f-deformed squeezed vacuum state|ξ, f even and f-deformed squeezed first excited state |ξ, f odd, which according to their production processes, essentially include only even and odd bases of Fock space, respectively. In the continuation, we introduce the superposition of these two distinct nonlinear squeezed states with a respective phase ?. Then, some of the criteria which imply the nonclassicality of the states, such as Mandel parameter, second-order correlation function, quadrature squeezing, amplitude-squared squeezing, Husimi and Wigner–Weyl quasi-distribution functions, are numerically examined. At last, by considering a well-known nonlinearity function associated with a nonlinear physical system, we present our results which outcome from the numerical calculations. It is shown that, the introduced f-deformed states can reveal high nonclassical features.
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