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

• URL: http://arxiv.org/abs/2603.26374v1
• Date: Fri, 27 Mar 2026 12:58:48 GMT
• Title: Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation
• Abstract summary: Superconductor-insulator-superconductor Josephson junction is the fundamental nonlinear element of superconducting circuits.<n> Connecting two junctions in series gives rise to higher-harmonic content in the total energy-phase relation.<n>We analyze the harmonic content of the double-junction element and discuss its sensitivity to charge noise.
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• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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