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

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|{iZ_j}>_q及其相反态|{-iZ_j}>_q的线性叠加所组成的第Ⅱ类两态叠加多模叠加态光场|ψ₂⁽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|ψ₂⁽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|ψ₂⁽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|ψ₂⁽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|ψ₂⁽²⁾>_q与态|ψ(2)1>_q这两者之间的压缩情况正好相反。

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

According to the linear superposition principle in quantum mechanics,we constructed the second kind of multi-mode light field state |ψ₂⁽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 |ψ₂⁽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 |ψ₂⁽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 |ψ₂⁽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 |ψ₂⁽²⁾>_q and the state |ψ (2) 1>_q is just contrary.