Multi-Directional Periodic Driving of a Two-Level System beyond Floquet Formalism

Quantum Physics arXiv:2511.03977 (quant-ph) [Submitted on 6 Nov 2025] Title:Multi-Directional Periodic Driving of a Two-Level System beyond Floquet Formalism Authors:Michael Warnock, David A. Hague, Vesna F. Mitrovic View a PDF of the paper titled Multi-Directional Periodic Driving of a Two-Level System beyond Floquet Formalism, by Michael Warnock and David A. Hague and Vesna F. Mitrovic View PDF HTML (experimental) Abstract:In this manuscript, we introduce an exact expression for the response of a semi-classical two-level quantum system subject to arbitrary periodic driving. Determining the transition probabilities of a two-level system driven by an arbitrary periodic waveform necessitates numerical calculations through methods such as Floquet theory, requiring the truncation of an infinite matrix. However, such truncation can lead to a loss of significant interference information, hindering quantum sensors or introducing artifacts in quantum control. To alleviate this issue, we use the $\star$-resolvent formalism with the path-sum theorem to determine the exact series solution to Schrödinger's equation, therefore providing the exact transition probability. The resulting series solution is generated from a compact kernel expression containing all of the information of the periodic drive and then expanded in a non-harmonic Fourier series basis given by the divided difference of complex exponentials with coefficients corresponding to products of generalized Bessel functions. The present method provides an analytical formulation for quantum sensors and control applications. Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2511.03977 [quant-ph] (or arXiv:2511.03977v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.03977 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Michael Warnock [view email] [v1] Thu, 6 Nov 2025 01:59:17 UTC (1,555 KB) Full-text links: Access Paper: View a PDF of the paper titled Multi-Directional Periodic Driving of a Two-Level System beyond Floquet Formalism, by Michael Warnock and David A. Hague and Vesna F. MitrovicView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: cond-mat cond-mat.mes-hall References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)