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Higher Josephson Harmonics in a Tunable Double-Junction Transmon Qubit

Ksenia Shagalov1,2,*, David Feldstein-Bofill1,2, Leo Uhre Jakobsen1,2, Zhenhai Sun1,2, Casper Wied1,2, Amalie T. J. Paulsen1,2, Johann Bock Severin1,2, Malthe A. Marciniak1,2, Clinton A. Potts1,2,3 et al.

Anders Kringhøj1,2, Jacob Hastrup1,2, Karsten Flensberg1, Svend Krøjer1,2, and Morten Kjaergaard1,2,†

  • *Contact author: ksenia.shagalov@nbi.ku.dk
  • †Contact author: mkjaergaard@nbi.ku.dk
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Phys. Rev. Lett. 137, 057001 – Published 28 July, 2026

DOI: https://doi.org/10.1103/fr7x-555s

Abstract

Tunable Josephson harmonics open new avenues for qubit design. We demonstrate a superconducting circuit element consisting of a tunnel junction in series with a superconducting quantum interference device (SQUID) loop, yielding a Josephson potential whose harmonic content is strongly tunable by magnetic flux. Through spectroscopy of the first four qubit transitions, together with an effective single-mode model renormalized by the internal mode, we resolve a second harmonic with an amplitude up to ∼10% of the fundamental. We identify a flux sweet spot where the ground-state dispersive shift vanishes, achieved by balancing the dispersive couplings to the internal and qubit modes. This highly tunable element provides a route toward protected qubits and customizable nonlinear microwave devices.

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Phys. Rev. Lett. 137, 057001– Published 28 July, 2026
  • Received 20 December 2025
  • Accepted 26 June 2026
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