The property of generalized nonlinear equal-order N-th power Y-squeezing in a new type of multi-mode light field state of superposition state with macroscopically distinct two quantum states

In this paper, the property of a new type of multi-mode light field state |ψ⁽²⁾msc>_q, which is composed of superposition state with macroscopically distinct two quantum states named the contrary state | {-Z_j}>_q of multi-mode (or q-mode) coherent state | {Z_j}>_q and the contrary state |{-iZ_j} >_q of multi-mode imaginary coherent state | {iZ _j}>_q respectively, is studied in detail by using the theory of multi-mode squeezed states established recently. It is found that: 1) if the squeezed order N=2p and p = 2m (m = 1, 2, 3, ⋯,⋯), the state |ψ⁽²⁾msc>_q is always stayed in the equal-order N-Y minimum uncertainty state; 2)if the squeezed order N = 2p and p = 2m+1(m = 0, 1, 2,⋯,⋯), while the quantization conditions are satisfied by the initial phase φ_j of each mode, by the initial phase difference between the two components in the state |ψ ⁽²⁾msc>_q and the sum Σ_j=1 ^qR_j² of average photon mumbers of all the single-mode coherent state light field |Z_j>, also by [(θ_nq^(R)- θ_nq^(I)) - Σ_j=1^qR_j²the state |ψ_msc⁽²⁾>_q can presents any order equal-order N-th power Y-squeezing effect which changes periodically; 3) if the squeezed order N is odd number, the state |ψ_msc ⁽²⁾>_q, under some certain conditions, is only stayed in the N-Y uncertainty state ; 4 ) partial squeezing degenerate phenomenon is found between the state |ψ_msc⁽²⁾>_q and the state |ψ⁽²⁾>_q, in References 21, which further show some objective coherent relation is the source of the phenomenon of squeezing degenerate.