Higher Josephson harmonics in a tunable double-junction transmon qubit

TL;DR

This paper demonstrates a superconducting circuit with tunable Josephson harmonics, revealing a significant second harmonic component and a flux sweet spot, advancing qubit design and nonlinear microwave device development.

Contribution

It introduces a novel tunable Josephson element with controllable harmonic content, including a prominent second harmonic, enabling new qubit protection schemes and device customization.

Findings

Second harmonic amplitude up to 10% of the fundamental.

Identification of a flux sweet spot with zero dispersive shift.

Effective single-mode model captures harmonic content and flux tunability.

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 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 $\sim10\%$ 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.