绝热和非绝热演化的简并快进标定理论  

Degenerate fast-forward scaling theory for adiabatic and non-adiabatic evolution

作　　者：杨青 刘忠菊[1] 李宏 张亚楠 YANG Qing;LIU Zhongju;LI Hong;ZHANG Yanan(School of Science,Shenyang University of Technology,Shenyang 110870,China;Institute for Interdisciplinary Quantum Information Technology,Jilin Engineering Normal University,Changchun 130052,China)

机构地区：[1]沈阳工业大学理学院,辽宁沈阳110870 [2]吉林工程技术师范学院量子信息技术交叉学科研究院,吉林长春130052

出　　处：《辽宁工程技术大学学报(自然科学版)》2024年第6期86-92,共7页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金项目(11947085);吉林省自然科学基金项目(YDZJ202201ZYTS324)。

摘　　要：为快速精确地控制复杂量子系统的演化,以简并的四能级量子系统为例,采用快进标定方法,得出不同状态下的加速势。在绝热演化过程中,将快进标定方法与无跃迁量子驱动方法融合,并应用于简并量子系统,得到简并量子系统的反绝热快进哈密顿量的一般形式。研究结果表明:快进态下的布居数转移时间相比标准态明显缩短,证明了快进标定方法在简并量子系统中的有效性。融合法中绝热项中的正则化项形式与简并无跃迁量子驱动哈密顿量形式完全对应,可有效提升系统的演化速率。研究结论为复杂量子系统控制和量子信息处理提供理论支撑。In order to control the evolution of complex quantum systems quickly and accurately,a degenerate four-level quantum system is taken as an example,and the acceleration potential in different states is obtained by using the fast-forward scaling method.In the adiabatic evolution process,the fast-forward scaling method is combined with the transitionless quantum driving,and the general form of the counterdiabatic fast-forward Hamiltonian of the degenerate quantum system is obtained.The results show that the population transfer time in the fast-forward state is significantly shorter than that in the standard state,which confirms the validity of the fast-forward scaling method in degenerate quantum systems.The regularization form of the adiabatic term in the combination method corresponds exactly to the form of the degenerate transitionless quantum driving Hamiltonian which can improve the rate of evolution of the system.The research conclusions provide theoretical support for complex quantum system control and quantum information processing.

关 键 词：快进标定方法 简并量子系统 无跃迁量子驱动方法 加速势 布居数 

分 类 号：O469[理学—凝聚态物理]