有限维Hilbert空间Roy型奇偶非线性相干态的振幅平方压缩

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 关键词： 有限维Hilbert空间 Roy型非线性相干态 奇偶非线性相干态 振幅平方压缩

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 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.