The property of generalized nonlinear equal-order higher-order n-th power h-squeezing of a new type of mscs light field with the superpositions of macroscopically distinct two quautum states

In this paper, the property of generalized nonlinear equal-order N-th power H-squeezing effect on a new type of multi-mode Schrödinger-Cat state (that is so-called MSCS) light field |ψ⁽²⁾>_q, with the superpositions of macroscopically distinct two quantum states | {Z_j} >_q, and | {Z_j}>_q respectively is further studied in detail, by utilizing the theory of multi-mode squeezed states established recently by Yang Zhiyong and Hou Xun and published in Acta Photonics Sinica from 1998. 4 to 1999. 5. It is found that 1) the MSCS |ψ(2)>_q is a typical nonclassical quantum light field state, if q · N, the products of squeezed order number N and cavity mode number q, is an even number or q · N=2p, but p = 2m′ + l (here p is an odd number, and m′ = 0, 1, 2, 3, ···, ···), while the quautization conditions are satisfied by the sum σ_j=1^qφ_j of the initial phases of all mode, by the initial phase difference (θ_pq(I)- θ_nq(R)) between the two components of the MSCS |φ(2)>_q, and by the whole average photon number σ_j=1^qR_j² of each multi-mode coherent state light field in the MSCS mentioned above (or, when the sum σR_j² changes continuously within a series of squeezed regions of the whole average photon number mentioned above), the MSCS |ψ⁽²⁾>_q can always displays the effects of any order generalized nonlinear equal-order N-th power H-squeezing, that changes periodically;2)the squeezed consequences (or the squeezed degree and squeezed depth) of both the first perpendicular component and the second perpendicular component of the MSCS |ψ⁽²⁾>_q are the same completely, the effects of the generalized nonlinear equal-order N-th power H-squeezing of the two perpendicular components mentioned can exchange periodically; and 3) compared with the Reference 16, the squeezed order number of the generalized nonlinear equal-order N-th power H-squeezing of the MSCS | ψ⁽²⁾>_q in this paper is even higher than the squeezed order number of the generalized nonlinear equal-order N-th power Y-squeezing of the MSCS in Reference 16.