Topological state engineering via supersymmetric transformations

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.