标题： 拓扑编织的布洛赫本征模，由非阿贝尔四元数不变量保护 显示英文标题

标题： Topological Braiding of Bloch Eigenmodes Protected by Non-Abelian Quaternion Invariants

摘要： 编织在物理学中引起了广泛关注，因为它在描述基本粒子交换方面起着重要作用。 将编织与拓扑保护相结合，可以使它对缺陷和扰动具有鲁棒性，但这种拓扑编织被认为只能在相互作用的量子系统中实现，例如拓扑超导体。 在这里，我们提出并展示了一种新的拓扑编织策略，该策略源于非阿贝尔拓扑绝缘体，这是一种最近发现的多带拓扑相。 我们揭示了编织与非阿贝尔四元数不变量之间的数学联系，通过这一联系，平行传输下的布洛赫本征模会产生由非阿贝尔能带拓扑保护的编织序列。 这种编织还与在布里渊区一半上量化几何相位有关。 这种新型的非阿贝尔拓扑编织在具有周期性合成维度的声学系统中被实验实现。 结果表明，这里发现的原理是一种新的拓扑编织策略，可以扩展到其他类型的经典波和非相互作用量子系统。 显示英文摘要

摘要： Braiding has attracted significant attention in physics because of its important role in describing the fundamental exchange of particles. Infusing the braiding with topological protection will make it robust against imperfections and perturbations, but such topological braiding is believed to be possible only in interacting quantum systems, e.g., topological superconductors. Here, we propose and demonstrate a new strategy of topological braiding that emerges from non-Abelian topological insulators, a class of recently discovered multi-band topological phase. We unveil a mathematical connection between braiding and non-Abelian quaternion invariants, by which Bloch eigenmodes under parallel transport produce braid sequences protected by the non-Abelian band topology. The braiding is also associated with geometric phases quantized over half the Brillouin zone. This new type of non-Abelian topological braiding is experimentally realized in acoustic systems with periodic synthetic dimensions. The results show that the principle discovered here is a new strategy towards topological braiding and can be extended for other types of classical waves and non-interacting quantum systems.