Wei-Norman分解及其在量子系统控制的应用  

Wei-Norman Decomposition and its Applications in Quantum System Control

作　　者：东宁[1] 丛爽[1] 

机构地区：[1]中国科学技术大学自动化系,安徽合肥230027

出　　处：《量子光学学报》2006年第4期242-247,共6页Journal of Quantum Optics

基　　金：安徽省教育厅自然科学基金资助项目(2003kj048zd)

摘　　要：W e i-Norm an分解对于分析矩阵微分方程的解是比较成熟的理论,含有幺正演化矩阵的薛定谔方程是矩阵微分方程,所以可以利用W e i-Norm an分解来分析求出多能级量子系统的解。由于W e i-Norm an分解适用的范围是小时间变化的邻域,为了求出量子系统在任意时刻的幺正演化矩阵,根据量子系统的特性,提出了对量子系统的控制时间进行分段,利用W e i-Norm an分解来获得每段小时间的幺正演化矩阵。最后通过一个两能级的例子进行仿真,根据实验结果总结出该量子系统的状态与控制场作用之间的关系。Wei-Norman decomposition is a well known theory for solving matrix differential equations. The Schroedinger Equation with unitary evolution equations is a matrix differential equations, so Wei-Norman decomposition can be used for solving the multi-level quantum systems. Owing to Wei-Norman decomposition＇s application being confined in a little time area, in order to obtain the Unitary evolution matrix at any time, a small division of time is proposed in this paper, and Wei-Norman decomposition is used in every small division to obtain the unitary evolution. Moreover, the proposed method can be used to a two-level quantum system. The relationship between the states of this quantum system and the control fields is given according to the simulation test results.

关 键 词：量子系统 Wei-Norman分解 李代数 幺正演化矩阵 

分 类 号：O431[机械工程—光学工程]