Study on the the properties of both generalized nonlinear equal-order N-th power Y-squeezing and generalized nonlinear equal-order N-th power H-squeezing in the third and the fourth kinds of multimode superposition state light field with the superpositions of macroscopically distinct two quantum states - On the phenomena of similitude squeezing and degenerate squeezing

According to the linear superposition principle of quantum mechanics in this paper, it is constructed respectively the third kind of multimode superposition state light field mathematical equation presented composed of the linear superposition of multimode (or q-mode) coherent state mathematical equation presented and multimode vaccum state mathematical equation presented, and the fourth kind of multimode superposition state light field mathematical equation presented made of the linear superposition of the contrary state mathematical equation presented of the multimode coherent state mathematical equation presented and the multimode vaccum state mathematical equation presented mentioned above. By utilizing the theory of multimode squeezed states established recently by Yang Zhiyong and Hou Xun and published in Acta Photonica Sinica, the properties of both generalized nonlinear equal-order N-th power Y-squeezing and generalized nonlinear equal-order N-th power H-squeezing of the state mathematical equation presented and the state mathematical equation presented mentioned are studied firstly in detail. It is found that 1) if some certain quantization conditions are satisfied respectively by the initial phase mathematical equation presented (here j = 1,2,3, mellip;, ⋯ , q) of each mode, or by the initial phase sum mathematical equation presented, and by the initial phase difference (mathematical equation presented) between the two components mathematical equation presented and mathematical equation presented, the state mathematical equation presented, and the state mathematical equation presented, can always display any order generalized nonlinear equal-order N-th power Y-squeezing and N-th power H-squeezing that changes periodically, these show that the state mathematical equation presented and the state mathematical equation presented are two kinds of typical nonclasical multimode light fields; 2) if the corresponding complex probability amplitudes between the state mathematical equation presented and the state mathematical equation presented are not equal to each other, the state mathematical equation presented and the state mathematical equation presented can always present the 'similitude squeezing' of both equal-order N-th power Y-squeezing and equal-order N-th power H-squeezing; and 3) if the corresponding complex probability amplitudes mentioned above are equal to each other, the state mathematical equation presented and the state mathematical equation presented can always present the 'degenerate squeezing' of both equal-order N-th power Y-squeezing and equal-order N-th power H-squeezing.