The bulk–boundary correspondence, a fundamental principle relating the topological invariants of the bulk to the presence of edge states, is modified in periodically driven systems. Conventional bulk topological invariants are insufficient to predict the existence of topological edge modes in such systems. Although ultracold atoms provide excellent settings for clean realizations of Floquet protocols, the observation of real-space edge modes has so far remained elusive. Here we demonstrate an experimental protocol for realizing chiral edge modes in optical lattices through the periodic modulation of the tunnelling rate between neighbouring sites. In particular, we show how to efficiently prepare particles in edge modes in three distinct Floquet topological regimes in a periodically driven honeycomb lattice. Controlling the height and amplitude of the potential step, we characterize the emergence of edge modes and the dependence of their group velocity on the sharpness of the potential step. Our direct observation of topological edge modes provides a tool to study topological phases of matter in the presence of disorder and interactions, where conventional bulk observables are not applicable.

体-边界对应关系是将体的拓扑不变量与边缘态的存在联系起来的基本原理，在周期性驱动的系统中被修改。传统的体拓扑不变量不足以预测此类系统中拓扑边缘模式的存在。尽管超冷原子为 Floquet 协议的干净实现提供了极好的设置，但迄今为止对真实空间边缘模式的观察仍然难以捉摸。在这里，我们演示了一种通过相邻位点之间隧道速率的周期性调制来实现光学晶格中手性边缘模式的实验协议。特别是，我们展示了如何在周期性驱动的蜂窝晶格中以三种不同的 Floquet 拓扑机制有效地制备边缘模式的粒子。通过控制势阶的高度和幅度，我们描述了边缘模式的出现及其群速度对势阶锐度的依赖性。我们对拓扑边缘模式的直接观察提供了一种工具，可以在存在无序和相互作用的情况下研究物质的拓扑相，而传统的体可观测值不适用。