量子系统的有效维数鉴别和约化理论

J4 ›› 2012, Vol. 29 ›› Issue (3): 316-322.

量子系统的有效维数鉴别和约化理论

徐强^1,2，双丰¹

1 中国科学院合肥智能机械研究所, 安徽合肥 230031;
2 中国科学技术大学自动化系, 安徽合肥 230026

收稿日期:2011-06-02 修回日期:2011-12-09 出版日期:2012-05-28 发布日期:2012-05-22
通讯作者: 双丰（1973-），湖南人，研究员，中国科学院百人计划入选者，从事量子控制和量子传感器研究。 E-mail:fshuang@iim.ac.cn
作者简介:徐强（1983-），安徽人，博士生，从事量子控制研究。E-mail: qxu@mail.ustc.edu.cn
基金资助:
自然科学基金(61074052，61072032), 中国科学院合肥物质研究院院长基金

Identification and reduction of effective dimensions of quantum systems

XU Qiang^1,2, SHUANG Feng¹

1 Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, 230031, China;
2 Department of Automation, University of Science and Technology of China, Hefei 230026, China

Received:2011-06-02 Revised:2011-12-09 Published:2012-05-28 Online:2012-05-22

摘要/Abstract

摘要：

考虑在外界激光脉冲控制下的含近简并能级的多能级系统的量子动力学，该多能级系统模型包括了一个基态和多个激发态，其中假设基态与各个激发态之间都存在跃迁。研究了不同激光脉冲场控制下的基态到近简并多能级激发态的布居转移。研究表明，在脉冲激光很短时，所考虑的多能级系统可以约化为一个二能级系统，并得到了在激光脉冲为多频弱场和单频强场时有效二能级系统参数的近似解析公式。以上结果可以推广到有多组近简并能级的多能级系统，用来鉴别有效控制维数，简化设计系统的控制策略。

关键词: 量子控制, 布居转移, 激光脉冲, 维数约化

Abstract:

Considering dynamics of a pulse-driven finite-dimensional quantum system with near degenerate eigenstates, the multi-level system includes one ground state and a number of excited states, in which the transitions exist between the ground state and any excited state. Population transfer induced by different kinds of pulses in this multi-level system were investigated. It is noted that in the case of both weak and strong fields, the quantum system can be reduced to a two-level system. Analytical relations between the original system and the reduced system are obtained for weak fields with multi frequencies and strong fields with one frequency. These results could be generalized to a multi-level system with several sets of near-degenerated eigenstates, and the conclusion could be utilized to identify the effective dimension of a quantum multi-level system controlled by laser.

Key words: quantum control, population transfer, laser pulses, dimension reduction

中图分类号:

O431.2

徐强双丰. 量子系统的有效维数鉴别和约化理论[J]. J4, 2012, 29(3): 316-322.

XU Qiang, SHUANG Feng. Identification and reduction of effective dimensions of quantum systems[J]. J4, 2012, 29(3): 316-322.

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