【摘要】 本文根据量子力学中的线性叠加原理 ,构造了由受量子相位调制的多模 (即 q模 )虚相干态 |{im1 Zj}〉q及其相反态 |{- im2 Zj}〉q这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场 |ψ( 2 )m1 ,m2 〉q.利用新近建立的多模压缩态理论 ,详细研究了态 |ψ( 2 )m1 ,m2 〉q的广义非线性等阶 N次方 Y压缩特性 .结果发现 :1 )无论态间的初始相位差 (θm2 - θm1 )、各模的初始相位 φj、腔模总数 q、压缩参量 Rj以及两态叠加的几率幅 rm1 和 rm2 等取何值 ,无论压缩阶数N取奇还是取偶 ,只要相位调制因子 m1和 m2 与压缩阶数 N的关系满足一定的量子化条件 ,态 |ψ( 2 )m1 m2 〉q就恒处于等阶 N- Y最小测不准态 .2 )当态间的初始相位差 (θm2 - θm1 )在态间压缩区 [2 kθπ-π/ 2 + qj =1{R2jsin[(m2 - m1)π/ 2 ]},2 kθπ+π/ 2 + qj =1{R2jsin[(m2 - m1)π/ 2 ]}]内取值时 ,无论压缩阶数 N取奇还是取偶 ,只要相位调制因子 m1和 m2 与 N的关系式以及各模的初始相位φj等满足一定的量子化条件 ,态 |ψ( 2 )m1 ,m2 〉q就可呈现出周期性变化的 ,任意阶的等阶 N次方 Y压缩效应 .3)利用相位调制因子 m1、m2 与压缩阶数 N之间的解析关系式 ,可直接确定出 |ψ( 2 )m1 m2 〉q呈现等阶 N次方 Y压缩效应时的压?更多还原

【Abstract】 According to the linear superposition principle in quantum mechanics,it is constructed a new kind of multi mode light field state ｜ψ (2) m 1m 2 〉 q which is made of linear superpositions of macroscopically distinct two quantum states named multi mode (or q mode) imaginary coherent states ｜｛i m′ Z j｝〉 q modulated by quantum coefficient m 1 and the contrary state of multi mode imaginary coherent states ｜｛i m 2 Z j｝ q,also modutaled by quantum phase coefficient m 2,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 ｜ψ (2) m 1m 2 〉 q is studied firstly in deteil.It is found that:1)Whether the initial phase difference (θ m 2 -θ m 1 ) between the two components of the state ｜ψ (2) m 1m 2 〉 q changes,the initial phase φ j(j=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 r m 1 and r m 2 of superpositions of the macroscopically distinct two quantum states modulated by the two different quantum phase i m 1 and i m 2 (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 m 1 and the relation of the squeezed order number N and the second phase modulating coefficient m 2 are satisfied,the state ｜ψ (2) m 1m 2 〉 q is always stayed in the equal order N Y minimum uncertainty state.2)When the initial phase difference (θ m 2 -θ m 1 ) mentioned above changes,within the region 2k θπ-π/2+qj=1｛R 2 jsin[(m 2-m 1)π/2]｝,2k θπ+π/2+qj=1｛R 2 jsin[(m 2-m 1)π/2]｝,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 m 1 by the relation between the squeezed order number N and the second phase modulating coefficient m 2 and by the initial phase φ j(j=1,2,3,…,…) of all modes,the states ｜ψ (2) m 1m 2 〉 q 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 ｜ψ (2) m 1m 2 〉 q can be determined directly by utilizing the relation between the squeezed order N and the phase modulating coefficient m 1 and m 2.4)The results on their generalized nonlinear equal order N 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 m 1 and m 2 satisfy the following conditions:m 1=m 2=0;m 1=m 2=1 and m 1=1,m 2=2 respectively.更多还原