Disorder-immune momentum band winding topology

TL;DR

This paper reveals a novel form of topological physics in complex momentum bands that are immune to disorder, demonstrated through photonic quantum walks and potentially useful for robust photonic applications.

Contribution

It uncovers a new disorder-immune topological phenomenon in complex momentum bands, distinct from known topological effects, with experimental and theoretical insights.

Findings

Momentum bands can wind topologically, causing localization at time interfaces.

The topology remains immune to arbitrarily strong disorder.

Extreme spatiotemporal randomness can destroy this topological phase.

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.