有限维Hilbert空间Roy型奇偶非线性相干态的振幅平方压缩

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

构造出了有限维Hilbert空间Roy型奇偶非线性相干态,讨论了它们的正交归一完备性和振幅平方压缩效应.研究表明,在此空间中Roy型奇偶非线性相干态是归一完备的,但不具有正交性;当复参数相位角θ满足一定条件时它们存在振幅平方压缩效应,同时导出了压缩条件与参数s,r以及函数f(n)之间的关系.最后借助于数值计算,发现对于5维(或7维)Hilbert空间中Roy型偶(或奇)非线性相干态,当参数θ和Lamb-Dike参数η取某一给定值时,在参数r变化的不同取值范围内,它们均可以呈现振幅平方压缩效应.

The Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space are constructed. Their amplitudesquared 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 θ of parameter β 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, θ and Lamb-Dike parameter η are given as the fixed value.