Emergent Harmonics in Josephson Tunnel Junctions Due to Series Inductance

TL;DR

This paper investigates the origin of higher-order harmonics in Josephson tunnel junctions, demonstrating that trace inductance significantly contributes to these harmonics, which impacts the design of superconducting quantum circuits.

Contribution

The study introduces a method to distinguish harmonic sources in Josephson junctions and shows that trace inductance is the primary cause of observed second harmonics.

Findings

Second harmonic scales with junction size

Trace inductance is the main source of harmonics

Spectroscopy confirms the second harmonic contribution

Abstract

Josephson tunnel junctions are essential elements of superconducting quantum circuits. The operability of these circuits presumes a $2\pi$-periodic sinusoidal potential of a tunnel junction, but higher-order corrections to this Josephson potential, often referred to as "harmonics," cause deviations from the expected circuit behavior. Two potential sources for these harmonics are the intrinsic current-phase relationship of the Josephson junction and the inductance of the metallic traces connecting the junction to other circuit elements. Here, we introduce a method to distinguish the origin of the observed harmonics using nearly-symmetric superconducting quantum interference devices (SQUIDs). Spectroscopic measurements of level transitions in multiple devices reveal features that cannot be explained by a standard cosine potential, but are accurately reproduced when accounting for a second-harmonic contribution to the model. The observed scaling of the second harmonic with Josephson-junction size indicates that it is due almost entirely to the trace inductance. These results inform the design of next-generation superconducting circuits for quantum information processing and the investigation of the supercurrent diode effect.