Topological charges and parity selection at Floquet quasienergy degeneracies
Abstract
The quasienergy spectrum of a strongly driven two-level system as a function of the driving parameters exhibits conical intersections, which are enabled by hidden time-nonlocal symmetries. We show that each such crossing carries a quantized topological charge: the Floquet--Berry phase acquired along an adiabatic loop around a cone is equal to a ℤ2-valued charge. We further identify a second family of degeneracies that occurs at vanishing driving amplitude, when the level splitting matches m energy quanta of the field. Along the Stark-shifted resonance line, the minimum quasienergy gap opens as |A|m, and the charge is nontrivial only for odd m. We analytically derive both results from a perturbative reduction to a spin-1/2 in an effective two-dimensional magnetic field and confirm them numerically through the Bargmann invariant. Moreover, we propose a chirality-based protocol that cancels the dynamical phase to isolate the geometric one, and an ancilla-based Ramsey readout that renders the topological charge directly observable.
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BibTeX
@misc{kohler2026topological,
title = {{Topological charges and parity selection at Floquet quasienergy degeneracies}},
author = {Sigmund Kohler and David Guéry-Odelin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00975},
eprint = {2609.00975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00975},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological charges and parity selection at Floquet quasienergy degeneracies
AU - Sigmund Kohler
AU - David Guéry-Odelin
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00975
UR - https://arxiv.org/abs/2609.00975
AB - The quasienergy spectrum of a strongly driven two-level system as a function of the driving parameters exhibits conical intersections, which are enabled by hidden time-nonlocal symmetries. We show that each such crossing carries a quantized topological charge: the Floquet--Berry phase acquired along an adiabatic loop around a cone is equal to a ℤ_2-valued charge. We further identify a second family of degeneracies that occurs at vanishing driving amplitude, when the level splitting matches m energy quanta of the field. Along the Stark-shifted resonance line, the minimum quasienergy gap opens as |A|^m, and the charge is nontrivial only for odd m. We analytically derive both results from a perturbative reduction to a spin-1/2 in an effective two-dimensional magnetic field and confirm them numerically through the Bargmann invariant. Moreover, we propose a chirality-based protocol that cancels the dynamical phase to isolate the geometric one, and an ancilla-based Ramsey readout that renders the topological charge directly observable.
ER -