Multimode entangled state with three states superposition on the (N+1)-dimensional Hilbert space and their N-th power difference squeezing properties
Wenhui Chen, Sun Zhong-yu · Jiguang zazhi · 2007
According to the principle of linear suporposition of quantum mechanics,the multimode entangled states ｜｛Ψ~((3))_(2q) is formed by linearly superposing three quantum states: the multimode complex conjugate coherent state ｜｛iZ~_j｝_(2q),multimode complex conjugate imaginary coherent state ｜｛iZ~_j｝_(2q) and multimode vacuum state ｜｛0_j｝_(2q) on the finite-dimensional(N+l) Hilbert space.and their difference squeezing properties of generalized nonlinear equal-power N-th power is studied by utilizing the general theory of multimode squeezed states.The results show that on the finite-dimensional Hilbert space,while some conditions are satisfied,the two quadratures of the state ｜Ψ~((3))_(2q) present the equal-power N-th power difference squeezing properties,but under some other conditions,the difference squeezing effects of two quadratures can be displayed at the same time,and the squeezed depth or squeezed degree in this space is different from that on the full-dimensional Hilbert space.It is called two-sided difference squeezing.