Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation

Quantum Physics [Submitted on 27 Mar 2026] Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation Leo Uhre Jakobsen, Ksenia Shagalov, David Feldstein-Bofill, Morten Kjaergaard, Karsten Flensberg, Svend Krøjer 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: 11 pages, 5+2 figures 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 Submission history From: Leo Uhre Jakobsen [view email] [v1] Fri, 27 Mar 2026 12:58:48 UTC (783 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)