Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation
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Quantum Physics arXiv:2603.26374 (quant-ph) [Submitted on 27 Mar 2026] Title:Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation Authors:Leo Uhre Jakobsen, Ksenia Shagalov, David Feldstein-Bofill, Morten Kjaergaard, Karsten Flensberg, Svend Krøjer View a PDF of the paper titled Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation, by Leo Uhre Jakobsen and 5 other authors View PDF Abstract:The superconductor-insulator-superconductor Josephson junction is the fundamental nonlinear element of superconducting circuits. Connecting two junctions in series gives rise to higher-harmonic content in the total energy-phase relation, enabling new design opportunities in multimode circuits. However, the double-junction element hosts an internal mode whose spectrum is set by the finite capacitances of the individual junctions. Using a Born-Oppenheimer approximation that treats the additional mode as fast compared to the qubit mode, we analyze the double-junction circuit element shunted by a large capacitor. Here, we derive an effective single-mode model of the qubit containing a correction term owing to the presence of the internal mode. We explore experimentally relevant parameter regimes and find that our model accurately describes the low-energy spectrum of the qubit. We further discuss how eliminating the internal degree of freedom affects the system's periodic boundary conditions and how this leads to non-uniqueness in performing the Born-Oppenheimer approximation. Finally, we analyze the harmonic content of the double-junction element and discuss its sensitivity to charge noise. Comments: Subjects: Quantum Physics (quant-ph) Report number: NBI QDEV 2026 Cite as: arXiv:2603.26374 [quant-ph] (or arXiv:2603.26374v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.26374 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Leo Uhre Jakobsen [view email] [v1] Fri, 27 Mar 2026 12:58:48 UTC (783 KB) Full-text links: Access Paper: View a PDF of the paper titled Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation, by Leo Uhre Jakobsen and 5 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)