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 $\mathbb{Z}_2$-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.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2609.00975 [cond-mat.mes-hall]

(or arXiv:2609.00975v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2609.00975 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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