标题： Floquet 光子晶格中外禀拓扑相的观测 显示英文标题

标题： Observation of extrinsic topological phases in Floquet photonic lattices

摘要： 离散步长行走描述了格点中粒子的动力学行为，这些粒子在离散时间发生跳跃或分裂事件。尽管对量子行走的物理特性来说具有首要兴趣，但由其离散步长特性产生的拓扑性质几乎尚未被探索。我们在此报告了离散步长行走特有的拓扑相位的观测结果。我们使用双光纤环路设置中的光脉冲，其动力学映射到一个二维格点上，并受到离散分裂事件的影响。我们展示了边缘态的数量不仅仅由格点的体不变量（即陈数和弗洛凯缠绕数）决定，这与静态格点和受平滑调制的格点的情况不同。边缘态的数量还由与作用于格点边界的离散步长幺正算符相关的拓扑不变量所确定。这种情况超出了通常的体-边对应关系，并允许操纵边缘态的数量而无需经历能隙闭合转变。我们的工作为工程化量子行走中粒子的拓扑模式开辟了新的视角。 显示英文摘要

摘要： Discrete-step walks describe the dynamics of particles in a lattice subject to hopping or splitting events at discrete times. Despite being of primordial interest to the physics of quantum walks, the topological properties arising from their discrete-step nature have been hardly explored. Here we report the observation of topological phases unique to discrete-step walks. We use light pulses in a double-fibre ring setup whose dynamics maps into a two-dimensional lattice subject to discrete splitting events. We show that the number of edge states is not simply described by the bulk invariants of the lattice (i.e., the Chern number and the Floquet winding number) as would be the case in static lattices and in lattices subject to smooth modulations. The number of edge states is also determined by a topological invariant associated to the discrete-step unitary operators acting at the edges of the lattice. This situation goes beyond the usual bulk-edge correspondence and allows manipulating the number of edge states without the need to go through a gap closing transition. Our work opens new perspectives for the engineering of topological modes for particles subject to quantum walks.