| 引用本文: | 闫家臻,匡森,陈蒙西,丛爽.给定环境下稳定开放量子系统的哈密顿量方法[J].控制理论与应用,2017,34(11):1506~1513.[点击复制] |
| YAN Jia-zhen,KUANG Sen,CHEN Meng-xi,CONG Shuang.Hamiltonian method for the stabilization of open quantum systems with given dissipations[J].Control Theory and Technology,2017,34(11):1506~1513.[点击复制] |
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| 给定环境下稳定开放量子系统的哈密顿量方法 |
| Hamiltonian method for the stabilization of open quantum systems with given dissipations |
| 摘要点击 2538 全文点击 1350 投稿时间：2017-08-29 修订日期：2017-11-25 |
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| DOI编号 10.7641/CTA.2017.70607 |
| 2017,34(11):1506-1513 |
| 中文关键词 开放量子系统 模型变换 哈密顿量设计 稳定化 相干矢量 |
| 英文关键词 open quantum systems model transform Hamiltonian design stabilization coherence vector |
| 基金项目 安徽省自然科学基金项目(1708085MF144), 国家自然科学基金项目(61773370, 61573330) |
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| 中文摘要 |
| 针对耗散已知情况下Lindblad主方程描述的开放量子系统, 本文通过哈密顿量的设计实现了系统对于目标
平衡态的稳定化. 借助相干矢量体系, 将矩阵形式下的原始系统模型转换为了一个矢量形式的线性系统, 并证明了
变换前后系统稳定属性的等价性. 通过保证矢量化线性系统模型的稳定性, 并使系统的唯一平衡态等于期望的目
标态, 得到了系统哈密顿量的设计框架. 特别地, 本文讨论了这两类条件下系统哈密顿量各元素的范围, 并指出根
据它们的交集即可构成所设计的系统哈密顿量. 最后, 在一个两能级系统上进行了数值仿真实验, 验证了本文哈密
顿量稳定化方案的有效性. |
| 英文摘要 |
| For open quantum systems described by the Lindblad master equation under given dissipations, this paper
achieves the stabilization of the target equilibrium state by designing the system Hamiltonians. Via the coherence vector
framework, the original matrix system model is transformed into a vector linear system and their stability equivalence is
proved. By guaranteeing the stability of the vectorized linear model and letting its unique equilibrium state equal the desired
target state, a frame for the design of the system Hamiltonian is obtained. In particular, this paper discusses the value range
of the elements of the system Hamiltonian under these two conditions and points out that the system Hamiltonian can be
obtained from their intersection set. Numerical simulation experiments on a two level system verify the effectiveness of the
proposed Hamiltonian stabilization scheme. |
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