Towards Extracting the Current-Phase Relation of Josephson Junctions With On-Wafer Microwave Probing and Calibration Techniques*

Josephson junctions (JJs) - two superconducting electrodes separated by a thin non-superconducting barrier - are integral components in superconducting quantum circuits used in many applications, such as computing and metrology. The supercurrent that flows across the barrier depends on the phase difference between the electrodes, known as the current-phase relation (CPR) and is typically assumed to be sinusoidal. Nevertheless, skewing occurs in junctions with various barrier compositions, such as normal metals and ferromagnets, which can significantly affect the output of devices. The CPR is commonly measured using superconducting quantum interference devices (SQUIDs). However, SQUIDs are very sensitive to flux noise which can limit their ability to measure the CPR. Here, we develop a novel SQUID-less approach to extract the CPR by using on-wafer microwave probing and calibration techniques. We extract the current-dependent Josephson inductance to reconstruct the CPR from measurements on niobium-silicide barrier JJ arrays embedded in superconducting coplanar waveguides. Upon validation, this novel approach would enable broadband, low noise measurements of the CPR by labs without SQUID measurement circuitry, making critical design information accessible for JJ circuits.