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Fast-driving spectroscopy of current-phase relationships of individual Josephson elements

Maxim Tjøtta1,*,†, Devashish Shah2,*, Kanishk Modi2,3, Marco Valentini2,4, Rubén Seoane Souto5, Georgios Katsaros2, and Jeroen Danon1

  • *These authors contributed equally to this work.
  • †Contact author: maxim.tjotta@ntnu.no

Phys. Rev. Applied 26, 044017 – Published 6 October, 2026

DOI: https://doi.org/10.1103/d3gl-qntm

Abstract

Extracting the current-phase relationship (CPR) of a single superconducting junction is challenging in practice and traditionally involves embedding the junction in a larger superconducting circuit containing SQUIDs and/or resonators. Applying ac driving to the junction has proven to be a viable and less invasive way to extract information about the few lowest harmonics of the CPR, by locating the integer and fractional Shapiro steps in the IV-curve of the driven junction. Here, we present an alternative driving-based method that allows to extract the full harmonic content of a CPR in a relatively noninvasive way, by fitting the measured critical currents of the driven junction as a function of driving power. We test our method, both using numerical simulations and in experiments, and we show that it works accurately.

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