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arXiv · 2603.26374

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
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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. In experimentally relevant parameter regimes, we numerically 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 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.

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Leo Uhre Jakobsen, Ksenia Shagalov, David Feldstein-Bofill, Morten Kjaergaard, Karsten Flensberg, Svend Krøjer. 2026-07-12. Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation. https://arxiv.org/abs/2603.26374

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