Cyclic ladder operators and hidden Weyl-Heisenberg structure in a Floquet system
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Quantum Physics arXiv:2606.06810 (quant-ph) [Submitted on 5 Jun 2026] Title:Cyclic ladder operators and hidden Weyl-Heisenberg structure in a Floquet system Authors:Tianao Wu, Li Ge View a PDF of the paper titled Cyclic ladder operators and hidden Weyl-Heisenberg structure in a Floquet system, by Tianao Wu and Li Ge View PDF HTML (experimental) Abstract:Ladder operators, found in the quantum harmonic oscillator and other quantized systems, provide an elegant approach to solving or understanding otherwise intricate physics problems. In this Letter, we discuss cyclic ladder operators in both Hermitian and non-Hermitian systems with a finite Hilbert space, with the highest (lowest) level directly descending (ascending) to the lowest (highest) level via a single raising (lowering) operation. We show that an equally spaced energy ladder emerges when these systems have an underlying Weyl-Heisenberg commutation relation, with the cyclic ladder operators and the temporal evolution operator behaving as the generators of the Weyl-Heisenberg group. We further illustrate such a system using a one-dimensional Floquet lattice, where the cyclic ladder operators become diagonal and the temporal evolution simplifies to a permutation matrix after a Floquet period. Our findings reveal a hidden relation between non-trivial dynamics and algebraic principles in Floquet systems, which may exist for other quantum numbers as well besides the energy levels. Comments: Subjects: Quantum Physics (quant-ph); Optics (physics.optics) Cite as: arXiv:2606.06810 [quant-ph] (or arXiv:2606.06810v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.06810 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Li Ge [view email] [v1] Fri, 5 Jun 2026 01:24:31 UTC (415 KB) Full-text links: Access Paper: View a PDF of the paper titled Cyclic ladder operators and hidden Weyl-Heisenberg structure in a Floquet system, by Tianao Wu and Li GeView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: physics physics.optics 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?) 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?)