Observation of topological phase with critical localization in a quasi-periodic lattice

TL;DR

This paper experimentally explores a topological phase in a critically localized regime within a quasi-periodic lattice, revealing unique localization and topological properties influenced by interactions, using ultracold atoms and momentum-lattice engineering.

Contribution

It introduces the first experimental observation of a topological phase with critical localization in a quasi-periodic lattice, advancing understanding of many-body critical phases.

Findings

Identification of topological phase in critically localized states

Demonstration of the impact of interactions on critical topological states

Implementation of momentum-lattice engineering with ultracold atoms

Abstract

Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce topology from trivial band structures, wherein topological invariants are shared by completely localized states in real space. Here we experimentally investigate a fundamentally distinct scenario where a topological phase is identified in a critically localized regime, with eigenstates neither fully extended nor completely localized. Adopting the technique of momentum-lattice engineering for ultracold atoms, we implement a one-dimensional, generalized Aubry-Andr\'e model with off-diagonal quasi-periodic disorder in momentum space, and characterize its localization and topological properties through dynamic observables. We then demonstrate the impact of interactions on the critically localized topological state, as a first experimental endeavour toward the clarification of many-body critical phase, the critical analogue of the many-body localized state.