Sigmund Kohler
Quantum Advanced Research Center
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Topological charges and parity selection at Floquet quasienergy degeneracies

Sigmund Kohler and David Guéry-Odelin
arXiv:2609.00975
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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last modified: 2.9.2026 by Sigmund Kohler