Anomalous multi-gap topological phases in periodically driven quantum rotors

TL;DR

This paper explores how periodically driven quantum rotors can host complex multi-gap topological phases with non-Abelian braiding, leading to novel out-of-equilibrium topological states observable in current experimental setups.

Contribution

It introduces a new platform using quantum rotors to realize and study multi-gap topological phases with non-Abelian properties and out-of-equilibrium phenomena.

Findings

Identification of non-Abelian braiding of band degeneracies.

Discovery of an anomalous Dirac string phase in strongly driven regimes.

Edge states at zero angular momentum indicating topological non-triviality.

Abstract

We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multi-gap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of band degeneracies. By adiabatically varying the periodic kicks to the rotor we find nodal-line braiding, which causes sign flips of topological charges of band nodes and can prevent them from annihilating, indicated by non-zero values of the %non-Abelian patch Euler class. In particular, we report on the emergence of an anomalous Dirac string phase arising in the strongly driven regime, a truly out-of-equilibrium phase of the quantum rotor. This phase emanates from braiding processes involving all (quasienergy) gaps and manifests itself with edge states at zero angular momentum. Our results reveal direct applications in state-of-the-art experiments of quantum rotors, such as linear molecules driven by periodic far-off-resonant laser pulses or artificial quantum rotors in optical lattices, whose extensive versatility offers precise modification and observation of novel non-Abelian topological properties.