论文标题
用Lie代数解耦方法求解量子动力学
Solving quantum dynamics with a Lie algebra decoupling method
论文作者
论文摘要
量子技术开发的核心是对单个量子水平的量子系统的控制。从数学上讲，这是通过研究哈密顿人的研究以及使用方法在各种制度中解决量子系统动力学的方法来实现的。在这里，我们提出了通过使用Lie代数解耦定理来解决量子系统动力学的教学介绍。作为背景，我们包括针对普通物理学观众的谎言组和谎言代数的概述。然后，我们证明了定理，并将其应用于三个众所周知的线性和二次汉密尔顿的示例，这些实例经常出现在量子光学和相关字段中。结果是一组微分方程，这些方程描述了所有线性和二次单模汉密尔顿的最高斯动力学，并具有通用的时间依赖性相互作用项。我们还讨论了超越二次哈密顿人超越二次汉密尔顿人的脱钩定理的使用以及解决开放系统动力学的使用。
At the heart of quantum technology development is the control of quantum systems at the level of individual quanta. Mathematically, this is realised through the study of Hamiltonians and the use of methods to solve the dynamics of quantum systems in various regimes. Here, we present a pedagogical introduction to solving the dynamics of quantum systems by the use of a Lie algebra decoupling theorem. As background, we include an overview of Lie groups and Lie algebras aimed at a general physicist audience. We then prove the theorem and apply it to three well-known examples of linear and quadratic Hamiltonian that frequently appear in quantum optics and related fields. The result is a set of differential equations that describe the most Gaussian dynamics for all linear and quadratic single-mode Hamiltonian with generic time-dependent interaction terms. We also discuss the use of the decoupling theorem beyond quadratic Hamiltonians and for solving open-system dynamics.
