一种新型的两态叠加多模Schrdinger猫态光场的等阶N次方Y压缩

THE PROPERTY OF GENERALIZED NONLINEAR EQUAL-ORDER N-TH POWER Y-SQUEEZING IN A NEW TYPE OF MULTI-MODE SCHR■DINGER-CAT STATE LIGHT FIELD WITH THE SUPERPOSITIONS OF MACROSCOPICALLY DISTINCT TWO QUANTUM STATES

本文根据量子力学的线性叠加原理，构造了由多模（即q模时目平态的相反态|｛｛－Zj｝〉q及多模虚相干态|｛｛－Zj｝〉q这两者的线性叠加所组成的一种新型的多模Schrodinger猫态光场利用新近建立的多模压缩态理论，研究了态的N次方Y压缩效应,结果发现：①当压缩阶数N＝Zp且p＝2m（m＝1，2，3，…，…）时，态。总是恒处于N－Y最小测不准态；②当压缩阶数N＝2p且p＝2m＋1（m＝0，1，2，3，…，…）时，如果各模的初始相位，态间的初始相位差以及各单模相干态光场的平均光子数之总和等满足一定的量子化条件，则态可呈现出周期性变化的、任意阶的N次方Y压缩效应；③当压缩阶数N＝2P＇＋1时，无论p＇＝2m（m＝0，1，2，…，…）还是p＇＝2m＋1（m＝0，1，2，3，…，……），只要各模的初始相位满足一定的量子条件，则当两态叠加几率幅满足时，态就恒处于N－Y测不准态，始终不呈现N－Y最小测不准态和N次方Y压缩；而当时，态始终不呈现N－Y测不准态、N－Y最小测不准态和N次方Y压缩效应．

According to the linear superposition principle in quantum mechanics in this paper, it isconstructed a new type of multi-mode Schrodinger-Cat state light field which is made of thelinear superposition of macroscopically distinct two quantum states named the contrary state of multi - mode (or q - mode ) coherent state and the multi - mode imaginary coherent state respectively. By using the theory of multi - mode squeezed states established recently by YangZhiyong and Hou Xun in references 25 - 28, the property of generalized nonlinear equal-order N-thpower Y-squeezing of the state mentioned above is studied. It is found that 1)if the squeezedorder N= 2p and p= 2m (m= 1, 2, 3, .…,… ),the state is always stayed in the N-Y minimumuncertalnty state; 2) if the squeezed order N = 2p and p = 2m + 1 (m = 0, 1, 2, 3, …,… ), while thequantization conditions are satisfied by the initial phase of each mode by the initial phase difference between the two components in the state and by the sum of average photonmumbers of all the single-mode coherent state light field (here,j= 1, 2, 3,…,q),the multi-modeSchrodinger-Cat state can presents any order N-th power Y-squeezing effect which changesperiodically ;and 3),if the squeezed order N= 2p' + 1, whether p' = 2m (m = 0, 1, 2, 3, …, … ) or p' = 2m+1 (m = 0, 1, 2, 3, …,… ), meanwhile if some certain conditions of quantization are satisfied by theinitial phase of each mode, while the probability amplitudes satisfy , the state isonly stayed in the N-Y uncertainty state rather than the N-Y minimum uncertainty state,and ,while he N-Y uncertainty state,the N-Y minimum uncertainty state,and the N-th powerY-squeezing can never present.