The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical systems such as spin models and multiqubit entangled states. Here, we propose persistent homology as a tool for characterizing and optimizing band structures of periodic photonic media. Using the honeycomb photonic lattice Haldane model as an example, we show how persistent homology is able to reliably classify a variety of band structures falling outside the usual paradigms of topological band theory, including “moat band” and multi-valley dispersion relations, and thereby control the properties of quantum emitters embedded in the lattice. The method is promising for the automated design of more complex systems such as photonic crystals and Moiré superlattices.

中文翻译：

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使用持久同源性的光子能带结构设计

持久同源性的机器学习技术通过在一系列特征尺度上计算复杂系统或数据集的拓扑特征，对它们进行分类。应用持久性同源性来表征物理系统（例如自旋模型和多量子位纠缠态）的兴趣日益浓厚。在这里，我们提出持久的同源性，作为表征和优化周期性光子介质的能带结构的工具。以蜂窝光子晶格Haldane模型为例，我们展示了持久的同源性如何能够可靠地分类属于拓扑带理论的通常范式之外的各种带结构，包括““带”和多谷色散关系，从而控制嵌入晶格中的量子发射器的属性。