Observation of Josephson Harmonics in Tunnel Junctions

TL;DR

This paper demonstrates that higher Josephson harmonics, arising from inhomogeneous AlO$_x$ barriers, significantly affect the energy spectra of superconducting qubits, leading to improved modeling and potential enhancements in quantum device performance.

Contribution

It introduces a mesoscopic model accounting for Josephson harmonics, improving the accuracy of energy spectrum predictions in superconducting qubits.

Findings

Higher Josephson harmonics are present in AlO$_x$ tunnel junctions.

Including harmonics in models greatly improves agreement with experimental spectra.

Engineered harmonics can reduce qubit errors while maintaining anharmonicity.

Abstract

Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminum oxide (AlO$_x$) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current-phase relation. However, this relation is only expected to hold in the limit of vanishingly low-transparency channels in the AlO$_x$ barrier. Here we show that the standard current-phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunneling through an inhomogeneous AlO$_x$ barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlO$_x$-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and the associated errors in transmon qubits by an order of magnitude, while preserving their anharmonicity.