Observation of Josephson harmonics in tunnel junctions

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 aluminium oxide (AlOx) 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 expected to hold only in the limit of vanishingly low-transparency channels in the AlOx 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 tunnelling through an inhomogeneous AlOx 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 AlOx-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.

Dennis Willsch, Dennis Rieger, Patrick Winkel, Madita Willsch, Christian Dickel, Jonas Krause, Yoichi Ando, Raphaël Lescanne, Zaki Leghtas, Nicholas T. Bronn, Pratiti Deb, Olivia Lanes, Zlatko K. Minev, Benedikt Dennig, Simon Geisert, Simon Günzler, Sören Ihssen, Patrick Paluch, Thomas Reisinger, Roudy Hanna, Jin Hee Bae, Peter Schüffelgen, Detlev Grützmacher, Luiza Buimaga-larinca, Cristian Morari, Wolfgang Wernsdorfer, David P. DiVincenzo, Kristel Michielsen, Gianluigi Catelani, loan M. Pop