[论文解读] Symmetries and selection rules in Floquet systems: application to harmonic generation in nonlinear optics

Ofer Neufeld, Daniel K. Podolsky+1 more|Figshare|Jun 4, 2017

Laser-Matter Interactions and Applications参考文献 19被引用 56

一句话总结

这篇论文建立了一般的 Floquet 群论框架，以推导驱动系统中的基于动力学对称性的选择规则，并将其应用于高次谐波产生，预测驱动和介质的对称性如何约束谐波发射与极化。

ABSTRACT

Symmetry is one of the most generic and useful concepts in physics and chemistry, often leading to conservation laws and selection rules. For example, symmetry considerations have been used to predict selection rules for transitions in atoms, molecules, and solids. Floquet systems also demonstrate a variety of symmetries which are spatiotemporal (i.e. dynamical symmetries (DSs)). However, the derivation of selection rules from DSs has so far been limited to several ad hoc cases. A general theory for deducing the impact of DSs in physical systems has not been formulated yet. Here we explore symmetries exhibited in Floquet systems using group theory, and discover novel DSs and selection rules. We derive the constraints on a general system's temporal evolution, and selection rules that are imposed by the DSs. As an example, we apply the theory to harmonic generation, and derive tables linking (2+1)D and (3+1)D DSs of the driving laser and medium to allowed harmonic emission and its polarization. We identify several new symmetries and selection rules, including an elliptical DS that leads to production of elliptically polarized harmonics where all the harmonics have the same ellipticity, and selection rules that have no explanation based on currently known conservation laws. We expect the theory to be useful for manipulating the harmonic spectrum, and for ultrafast spectroscopy. Furthermore, the presented Floquet group theory should be useful in various other systems, e.g., Floquet topological insulators and photonic lattices, possibly yielding formal and general classification of symmetry and topological properties.

研究动机与目标

• 激励在 Floquet 系统中使用动力学对称性来预测物理约束。
• 建立一个通用的群理论框架，从动力学对称性推导选择规则。
• 将该框架应用于高次谐波产生，以将对称性与辐射通道和极化相关联。
• 识别超越传统守恒定律的新对称性和选择规则。
• 提出在超快光谱学和光子系统中的潜在应用。

提出的方法

• 为驱动系统中的时空对称性（动力学对称性）制定 Floquet 群论。
• 将对称性分类为由驱动激光场和介质产生的 2+1D 和 3+1D 的 DSs。
• 导出 DSs 对时间演化和选择规则的约束。
• 推导 DSs 与允许的谐波发射和极化之间的关系。
• 识别新的 DS，如椭圆形 DS，以及相应的椭圆极化的谐波。
• 提出一个适用于 Floquet 拓扑绝缘体和光子晶格的框架。

实验结果

研究问题

• RQ1 哪些动力学对称性（DSs）约束 Floquet 系统的演化？
• RQ2 DSs 如何限制非线性光学中的高次谐波产生过程？
• RQ3 驱动和介质的 (2+1)D/ (3+1)D DSs 与发射谐波之间的连接规则是什么？
• RQ4 新的 DSs 能否预测谐波的极化特性，超出已知的守恒定律？
• RQ5 如何利用 Floquet 群论框架来对相关系统中的对称性与拓扑性质进行分类？

主要发现

• 在 Floquet 系统中识别出新颖的动力学对称性。
• 推导将 DSs 与允许的谐波发射和极化联系起来的选择规则。
• 在椭圆形 DS 下预测椭圆偏振的谐波（所有谐波具有相同的椭率）。
• 发现了传统守恒定律无法解释的选择规则。
• 适用于其他 Floquet 系统的通用理论，如光子晶格和 Floquet 拓扑绝缘体。