Towards Microwave Calibration Techniques to Characterize the Current-Phase Relation of Josephson Junctions

The supercurrent through Josephson junctions (JJs) depends on the phase difference between the order parameters of the constituent superconducting electrodes. Generally, this current-phase relation (CPR) is assumed to be sinusoidal. However, junctions with barriers comprised of various materials, such as normal metals or ferromagnets, have demonstrated skewing behavior, which can cause significant deviations from the expected output of devices containing JJs. Superconducting quantum interference devices (SQUIDs) are commonly used to measure the CPR, however SQUIDs are very sensitive to flux noise and can easily couple to nearby circuit components. Here, we will use an independent technique based on on-wafer direct voltage and current waveform measurements at microwave frequencies to reconstruct the CPR by extracting the Josephson inductance of JJ array transmission lines as a function of bias current. We apply this approach to studying the CPR in niobium-doped amorphous silicon JJ arrays, in which preliminary SQUID data suggests evidence of skewing. Upon validation, this novel approach would enable broadband, low noise measurements of the CPR by labs without SQUID measurement capabilities, making critical design information accessible for JJ circuits.