Characterization of the Capacitance of Small Josephson Junctions from dc SQUID Resonances

Developing techniques for characterizing and targeting the parameters of small-area Josephson junctions is important for implementing large superconducting qubit arrays. In particular, the self-capacitance of shadow-evaporated small area junctions is often challenging to extract, yet it plays an important role in the development of various topologically protected qubit designs. A dc SQUID allows for the extraction of individual junction capacitances via the measurement of the LC self-resonance in the current-voltage characteristic. By varying the dc SQUID geometry, as well as the critical current densities of the Al-AlOx-Al junctions that make up the SQUID, we can measure the behavior of the self-resonance and characterize the specific capacitance of these small Josephson junctions.