The properties of generalized nonlinear equal-order N-H power Y-squeezing in a new kind of multi-mode light field state with superpositions of macroscopically distinct two defferent quantum phase

According to the linear superposition principle in quantum mechanics, it is constructed a new kind of multimode light-field state (mathematical equation) which is made of linear superpositions of macroscopically distinct two quantum states named multi-mode (or q-mode) imaginary coherent states (mathematical equation) modulated by quantum coefficient m₁ and the contrary state of multi-mode imaginary coherent states |(mathematical equation), also modutaled by quantum phase coefficient m₂₉, respectively in this paper. By using the theory of multi-mode squeezing state that is established recently by Yang Zhiyong and Hou Xun and published in Acta Photonica Sinica from 1998. 4 to 1999. 5, the generalized nonlinear equal-order N-th power Y-squeezing effects of the state (methametical equation) is studied firstly in deteil. It is found that:1) Whether the initial phase difference (mathematical equation) between the two components of the state (mathematical equation) changes, the initial phase (1, 2, 3,...,...,q) of all modes, the sum number of cavity-mode number q, the squeezing parameters R_j(j= 1, 2, 3,...,.... ,q) and the propability amplitudes mathematical equation and mathematical equation of superpositions of the macroscopically distinct two quantum states modulated by the two different quantum phase mathematical equation and mathematical equation(here i= √ - 1 etc,change,and whether the squeezed order number N is an odd number or an even number,while a series of quantization conditions between the relation of the squeezed-order number N and the first phase modulating coefficient m₁ and the relation of the squeezed-order number N and the second phase modulating coefficient m₂ are satisfied,the state mathematical equation is always stayed in the equal-order N-Y minimum uncertainty state. 2 ) When the initial phase difference (mathematical equation) mentioned above changes, within the region [mathematical equation],whether the squeezed-order number N is an odd number or an even number,while a series of the quantization conditions are satisfied by the relation between the squeezed-order number N and the first phase modulating coefficient mt by the relation between the queezed-order number N and the second phase modulating coefficient mz and by the initial phase mathematical equation(j=1,2,3,⋯ ,⋯) of all modes,the states (mathematical equation), always presents the effect of any order equal-order N-th power Y-squeezing,which changes periodically. 3) The squeezed-order number N of the equal-order N-th power Y-squeezing of the state (mathematical equation), can be determined directly by utilizing the relation between the squeezed-order N and the phase modulating coefficient mi and mi. 4)The results on their generalized nonlinear equal-order iv'-th power Y-squeezing of reference 2,11 and 15,published in Acta Photonica Sinica, appear to be only the specific examples of our paper, only when ni\ and m2 satisfy the following conditions:m₁=m₂0;m₁=m₂= 1 and m₁ = 1,m₂ = 2 respectively.