Amplitude-squared squeezing of Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space

The Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space are constructed. Their amplitude-squared squeezing effect, orthonormalized property, unitary property and completeness relations are discussed. The results reveal the existence of unitary property, completeness relations and non-orthonormalized property. There exists the amplitude-squared squeezing effect for the Roy-type even and odd nonlinear coherent states when the phase theta of parameter beta meets the fixed condition. The relations between conditions of squeezing effect and parameters s, r and function f(n) are given. Finally using the numerical method, it is found that in some different ranges of r, the amplitude-squared squeezing effect exists in Roy-type even and odd nonlinear coherent states field in a finite-dimensional Hilbert space when the parameters s, theta and Lamb-Dike parameter eta are given as the fixed value.