Disorder-immune momentum band winding topology

Abstract

Time is the odd dimension out: Unlike space, it follows the arrow of time, forbidding back-reflections and requiring momentum yet not energy conservation. Tailored temporal variations manipulate momentum bands and engineer waves in time. We show that momentum bands exhibit unique topology, hidden when conventionally considering energy bands: Complex momentum bands may wind, mandating topological localization at time interfaces. We observe this effect in photonic quantum walks and study it under disorder. Remarkably, unlike any known topological phenomenon, the topology is immune against arbitrarily strong disorder. Only exotic conditions through extreme spatiotemporally random non-Hermiticity can destroy it. Our findings uncover a disorder-immune type of topological physics, inviting explorations of complex momentum or energy-momentum topology with potential applications like ultrarobust lasing, temporal pulse shaping or amplification.