Title: Programmable lattices for non-Abelian topological photonics and braiding Show Chinese title

Title: 可编程晶格用于非阿贝尔拓扑光子学和编织

Abstract: Non-Abelian physics, originating from noncommutative sequences of operations, unveils novel topological degrees of freedom for advancing band theory and quantum computation. In photonics, significant efforts have been devoted to developing reconfigurable non-Abelian platforms, serving both as classical testbeds for non-Abelian quantum phenomena and as programmable systems that harness topological complexities. Here we establish topological spinor lattices for non-Abelian programmable photonics. We design a building block for reconfigurable unitary coupling between pseudospin resonances, achieving a universal set of rotation gates through coupling along the unit cell boundary. The lattice assembly of our building blocks enables the emulation of the extended quantum Hall family across various eigenspinor bases. Particularly, we reveal the emergence of a non-Abelian interface even when the bulks are Abelian, which allows the topologically trivial engineering of topologically protected edge states. We also define the braid group for pseudospin observables, demonstrating non-Abelian braiding operations and the Yang-Baxter relations. Our results pave the way for realizing a reconfigurable testbed for a wide class of Abelian and non-Abelian topological phenomena and braiding operations. Show Chinese abstract

Abstract: 非阿贝尔物理源于操作序列的非对易性，揭示了用于推进能带理论和量子计算的新拓扑自由度。 在光子学中，已经投入了大量努力来开发可重新配置的非阿贝尔平台，这些平台既作为非阿贝尔量子现象的经典测试平台，又作为利用拓扑复杂性的可编程系统。 在这里，我们为非阿贝尔可编程光子学建立了拓扑旋量晶格。 我们设计了一个用于伪自旋共振之间可重新配置酉耦合的构建模块，通过单元边界耦合实现了旋转门的通用集。 我们构建模块的晶格组装使得能够在各种本征旋量基上模拟扩展的量子霍尔家族。 特别是，我们揭示了即使体是阿贝尔的情况下，也会出现非阿贝尔界面，这允许拓扑平凡地工程化拓扑保护的边缘态。 我们还定义了伪自旋可观测量的辫群，展示了非阿贝尔辫操作和杨-巴克斯特关系。 我们的结果为实现广泛类别的阿贝尔和非阿贝尔拓扑现象及辫操作的可重新配置测试平台铺平了道路。