Topological charges and parity selection at Floquet quasienergy degeneracies

• URL: http://arxiv.org/abs/2609.00975v1
• Date: Tue, 01 Sep 2026 09:31:44 GMT
• Title: Topological charges and parity selection at Floquet quasienergy degeneracies
• Abstract summary: We find a family of degeneracies that occurs at vanishing driving amplitude.<n>Along the Stark-shifted resonance line, the minimum quasienergy gap opens as $|A|m$, and the charge is nontrivial only for odd $m$.<n>We propose a chirality-based protocol that cancels the dynamical phase to isolate the one, and an ancilla-based Ramsey readout that renders the topological charge directly observable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\mathbb{Z}_2$-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.

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