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Anomalous multigap topological phases in periodically driven quantum rotors

Volker Karle1,*, Mikhail Lemeshko1,†, Adrien Bouhon2,3, Robert-Jan Slager2,4,‡, and F. Nur Ünal2,5,§

  • *Contact author: volker.karle@ista.ac.at
  • †Contact author: mikhail.lemeshko@ista.ac.at
  • ‡Contact author: rjs269@cam.ac.uk
  • §Contact author: fnu20@cam.ac.uk
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Phys. Rev. A 113, 012216 – Published 12 January, 2026

DOI: https://doi.org/10.1103/db9d-9bns

Abstract

We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multigap 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 nonzero values of the 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.

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Phys. Rev. A 113, 012216– Published 12 January, 2026
  • Received 24 October 2025
  • Accepted 20 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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