Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving

TL;DR

This paper classifies topological steady states in quasiperiodically driven lattice models, revealing anomalous localized phases with unique edge states and energy pumping capabilities, extending topological understanding to driven, incommensurate systems.

Contribution

It introduces a topological classification of driven lattice models with incommensurate frequencies, uncovering anomalous phases and their observable signatures in low-dimensional systems.

Findings

Identification of quantized circulating currents in certain ALTPs

Discovery of topological edge states functioning as energy pumps

Design of models achieving multiple topological classes in driven systems

Abstract

We derive a topological classification of the steady states of $d$-dimensional lattice models driven by $D$ incommensurate tones. Mapping to a unifying $(d+D)$-dimensional localized model in frequency space reveals anomalous localized topological phases (ALTPs) with no static analog. While the formal classification is determined by $d+D$, the observable signatures of each ALTP depend on the spatial dimension $d$. For each $d$, with $d+D=3$, we identify a quantized circulating current, and corresponding topological edge states. The edge states for a driven wire ($d=1$) function as a quantized, nonadiabatic energy pump between the drives. We design concrete models of quasiperiodically driven qubits and wires that achieve ALTPs of several topological classes. Our results provide a route to experimentally access higher dimensional ALTPs in driven low-dimensional systems.