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

According to the linear superposition principle in quantum mechanics in this paper, it is constructed a new type of multi-mode superposition light field state ιψ_msc⁽²⁾>_q, which is made of the linear superposition of macroscopically distinct two quantum states named the contrary state ι {- Z_j}>_q of multi-mode (q-mode) coherent state ι {Z_j}>_q and the contrary state ι {- iZ_j}>_q of multi-mode imaginary coherent state ι {iZ_j}>_q repectively. By using the theory of multi-mode squeezed states established recently by Yang Zhiyong and Hou Xun, which was published in Acta Photonica Sinica from April 1998 to May 1999, the property of generalied nonlinear equal-order N-th power H-squeezing of the state ιψ_msc⁽²⁾>_q mentioned above is studied in detail. It is found that:l) if q · N=2p and p = 2m(m = l,2,3,···,···), the state ιψ_msc⁽²⁾>_q is always stayed in the N-H minimum uncertainty state;2) If q · N=2p and p = 2m′+ 1 Cm′= 0, 1, 2, 3, ···,···) when some certain quantization conditions are satisfied by the sum of initial phase of each mode σ_j=1^qφ_j(j=l, 2, 3,···,q), by the initial phase difference (θ_nq^(I)-θ_nq^(I)) between the two components in the state ψ_msc ⁽²⁾>_q, by σ_j=1^qR _j² the average photon numbers of all the single-mode coherent state light field and by [(θ_nq^(I)- θ_nq^(R)) + σ_j=1^qR _j², the state ιψ_msc ⁽²⁾>_q can presents any order N-th power H-squeezing effect which changes periodically; 3)if q · N = 2p + 1, whether p = 2m (m = 0,1,2,3, ···,···) or p- 2m′ +1 Cm′ = 0,1,2,3, ···,···), when the sum of initial phase of each mode satisfy some certain quantization conditions, and while the probability amplitudes satisfy r_nq ^(I)=r_nq^(I), the state ιψ _msc⁽²⁾>_q is only stayed in the N-H uncertainty state.