Topological memory of nonreciprocal scattering singularities

Non-Hermitian systems host a wealth of exotic phenomena, yet their temporal topology-particularly in time-reversal-symmetry-broken conditions-remains largely unexplored. Here, we experimentally demonstrate topological memory emerging from hysteresis-driven dynamics in a nonreciprocal microwave scattering system. The scattering singularity, encompassing both backscattering zeros and nonreciprocal exceptional points (EPs), serves as the cornerstone of this effect. Magnetic hysteresis induces a history-dependent trajectory of the complex scattering parameter that winds around such singularities, giving rise to quantized topological charges and sharp transitions when crossing them. At the limit of infinite nonreciprocity, backscattering zeros facilitate access to EPs, drastically easing their realization and yielding enhanced frequency combs near the transition. Extending these dynamics to free-space broadcasting and circulator-based topological insulators, we demonstrate nonreciprocity-assisted transport and long-distance preservation of scattering singularities. Our results uncover the interplay among singularity, nonreciprocity, and Floquet engineering, establishing a unified platform for exploring temporal topology and in-memory non-Hermitian photonics.