The quest to explore new techniques for the manipulation of topological states simultaneously promotes a deeper understanding of topological physics and is essential in identifying new ways to harness their unique features. Here, we examine the potential of supersymmetric transformations to systematically address, alter and reconfigure the topological properties of a system. To this end, we theoretically and experimentally study the changes that topologically protected states in photonic lattices undergo as supersymmetric transformations are applied to their host system. In particular, we show how supersymmetry-induced phase transitions can selectively suspend and re-establish the topological protection of specific states. Furthermore, we reveal how understanding the interplay between internal symmetries and the symmetry constraints of supersymmetric transformations provides a roadmap to directly access the desirable topological properties of a system. Our findings pave the way for establishing supersymmetry-inspired techniques as a powerful and versatile tool for topological state engineering.

同时探索探索操作拓扑状态的新技术的目的是促进对拓扑物理学的更深入了解，这对于确定利用其独特功能的新方法至关重要。在这里，我们研究了超对称变换潜在地系统地解决，改变和重新配置系统的拓扑特性的可能性。为此，我们在理论上和实验上研究了将光子晶格中的拓扑保护态应用于超对称变换时所经历的变化。特别是，我们展示了超对称性诱导的相变如何能够选择性地中止并重新建立特定状态的拓扑保护。此外，我们揭示了如何理解内部对称性和超对称变换的对称性约束之间的相互作用如何提供直接访问系统所需拓扑特性的路线图。我们的发现为建立超对称启发技术奠定了基础，该技术是拓扑状态工程的强大而通用的工具。