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 (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 expected to hold only 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 tunnelling 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 AlOx-based
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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.