Solid State Institute, Technion-Israel Institute of Technology, 32000, Haifa, Israel.
Physics Department, Technion-Israel Institute of Technology, 32000, Haifa, Israel.
Nat Commun. 2019 Jan 24;10(1):405. doi: 10.1038/s41467-018-07935-y.
Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.
对称性是科学中最通用和有用的概念之一，通常会导致守恒定律和选择规则。在这里，我们为时间周期性的 Floquet 系统中的动力学对称性（DS）制定了一个通用的群论，并推导出它们与可观测的选择规则之间的对应关系。我们将该理论应用于谐波产生，推导出了一个链接驱动激光和介质（气体、液体或固体）在（2+1）D 和（3+1）D 几何中的 DS 的封闭形式表格，将其与允许的和禁止的谐波阶数及其偏振联系起来。我们确定了对称性，包括基于时间反转、基于反射和基于椭圆的 DS，它们导致了目前已知的守恒定律无法解释的选择规则。我们预计该理论将对超快高次谐波对称性破坏光谱学有用，也将在其他各种系统中有用，如 Floquet 拓扑绝缘体。
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