The properties of generalized nonlinear equal-order N-th power H-squeezing in the fifth kind of multimode superposition state light field with the superpositions of macroscopically distinct two quantum states

In this paper, the properties of generalized nonlinear equal-order N-th power H-squeezing of the fifth kind of multimode superposition state light field |ψ₅⁽²⁾>_q that is composed of the linear superpositions of multimode vacuum state |{0_j}>_q and the contrary state |{-iZ_j}>_q of multimode imaginary coherent state |{iZ_j}>_q is studied in detail by utilizing the theory of multimode squeezed states suggested by Yang Zhiyong and Hou Xun and published in Acta Photonica Sinica. It is found that: 1) The state |ψ₅⁽²⁾>_q is a new type of multimode nonclassical light field, if some certain quantization conditions are satisfied respectively by the initial phase sum ∑_j=1^qφ_j of every mode, and by the initial phase difference (θ_nq^(I) - θ_0q^(o)) between the two components |{O_j}>_q and |{-iZ_j}>_q mentioned above, the state |ψ₅⁽²⁾>_q can always displays the four different forms of generalized nonlinear equal-order N-th power H-squeezing effects such as any odd-number-mode with odd-number-order, any odd-number-mode with even-number-order, any even-number-mode with even-number-order, and any even-number-mode with odd-number-order equal-order N-th power H-squeezing effects. 2) Because the squeezing conditions satisfied by the initial phase sum of every mode are not the same, the squeezed amplitude, the squeezed consequence, and the squeezed characteristic of the four different forms of equal-order N-th power H-squeezing effects presented by the state |ψ₅⁽²⁾>_q mentioned above are quite different through the squeezing conditions satisfied by the initial phase difference between the two components of the state |ψ₅⁽²⁾>_q are the same completely. 3) Whether the products q · N of the cavity-mode number q and the squeezing-order number N is an odd-number or an even-number, the generalized nonlinear equal-order N-th power H-squeezing effects displayed by the first perpendicular component and by the second one of the state |ψ₅⁽²⁾>_q can always present the relation of periodical reciprocation.