第Ⅱ类两态叠加多模叠加态光场的非线性高阶压缩特性研究

PROPERTIES OF NONLINEAR HIGHER ORDER SQUEEZING IN SECOND KIND OF MULTI MODE LIGHT FIELD STATE OF SUPERPOSITION STATE WITH DISTINGUISHABLE TWO QUANTUM STATES

本文根据量子力学中的线性叠加原理，构造了由多模（即ｑ模）虚相干态｜｛ｉＺｊ｝＞ｑ及其相反态｜｛－ｉＺｊ｝＞ｑ的线性叠加所组成的第Ⅱ类两态叠加多模叠加态光场｜ψ（２）２＞ｑ．利用新近建立的有关双模及多模辐射场的非线性高阶压缩理论，首次对态｜ψ（２）２＞ｑ的两种非线性高阶压缩（即Ｎ次方Ｙ压缩和Ｎ次方Ｈ压缩）效应进行了详细研究．结果表明：１）当Ｎ为奇数时，如果各模的初始相位满足一定的量子化条件，而态间的初始相位差在其态间压缩区内连续变化；或者态间的初始相位差取某一特定值，而各模的初始相位在其腔模压缩区内连续变化时，态｜ψ（２）２＞ｑ就会呈现出周期性变化的、任意阶的Ｎ次方Ｙ压缩效应．２）当ｑ·Ｎ为奇数时，如果各模的初始相位和满足一定的量子化条件，而态间的初始相位差在上述的态间压缩区内连续变化；或者态间的初始相位差取上述的某一固定值，而各模的初始相位和在其腔模和压缩区内连续变化时，态｜ψ（２）２＞ｑ就呈现出周期性变化的、任意阶的Ｎ次方Ｈ压缩效应．３）与文献１０相比，态｜ψ（２）２＞ｑ与态｜ψ（２）１＞ｑ这两者之间的压缩情况正好相反．

According to the linear superposition principle in quantum mechanics,we constructed the second kind of multi mode light field state |ψ (2) 2> q which is cemposed of the linear superposition with distinguishable two quantum states named multi mode (or q mode) imaginary coherent state |{iZ j}> g and its contrary state |{-iZ j}> g respectively in this paper.By using the nonlinear higher order squeezing theory of multi mode radiative light field which is established recently by Yang Zhiyong and Hou Xun in references 8～10,it is studied the two nonlinear higher order squeezing effects,both N th power Y squeezing and N th power H squeezing,of the state |ψ (2) 2> q firstly in detail.It is found that (1),if N=2p+1(p=0,1,2,3,…,…),when the initial phase of all modes satisfy their quantization condition and when the initial phase difference between the state |{iZ j}> q and the state |{-iZ j}> q changes continuously within its squeezing region,or when the initial phase diffevence between the states mentiened above equals a specific value and the initial phase of all modes changes continuously within its cavity mode squeezing region,the state |ψ (2) 2> q always presents and order N th power Y squeezing effect that changes periodically;(2),if q·N=2p+1(p=0,1,2,3,…,…),when the initial phase sum of all modes satisfy its quantization condition and the initial phase difference between state |{iZ j}> q and |{-iZ j}> q changes continuously within its another squeezing region,or the initial phase difference between state |{iZ j}> q and |{-iZ j}> q is equal to the specific value mentioned above and the initial phase sum of all modes changes continuously with its cavity mode sum squeezing region,the state |ψ (2) 2> q can always display any order N th power H squeezing which changes periodically too;(3),compared with the investigation in reference 10,both the behaviours and the conditions of nonlinear higher order squeezing between the state |ψ (2) 2> q and the state |ψ (2) 1> q is just contrary.