Tunable Josephson harmonics open new avenues for qubit design. We demonstrate a superconducting circuit element consisting of a tunnel junction in series with a 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 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.
@article{arxiv.2512.08470,
title = {Higher Josephson harmonics in a tunable double-junction transmon qubit},
author = {Ksenia Shagalov and David Feldstein-Bofill and Leo Uhre Jakobsen and Zhenhai Sun and Casper Wied and Amalie T. J. Paulsen and Johann Bock Severin and Malthe A. Marciniak and Clinton A. Potts and Anders Kringhøj and Jacob Hastrup and Karsten Flensberg and Svend Krøjer and Morten Kjaergaard},
journal= {arXiv preprint arXiv:2512.08470},
year = {2025}
}