Gate-tunable Josephson junctions embedded in a microwave environment provide a promising platform to in-situ engineer and optimize novel superconducting quantum circuits. The key quantity for the circuit design is the phase-dependent complex admittance of the junction, which can be probed by sensing an rf SQUID with a tank circuit. Here, we investigate a graphene-based Josephson junction as a prototype gate-tunable element enclosed in a SQUID loop that is inductively coupled to a superconducting resonator operating at 3 GHz. With a concise circuit model that describes the dispersive and dissipative response of the coupled system, we extract the phase-dependent junction admittance corrected for self-screening of the SQUID loop. We decompose the admittance into the current-phase relation and the phase-dependent loss and as these quantities are dictated by the spectrum and population dynamics of the supercurrent-carrying Andreev bound states, we gain insight to the underlying microscopic transport mechanisms in the junction. We theoretically reproduce the experimental results by considering a short, diffusive junction model that takes into account the interaction between the Andreev spectrum and the electromagnetic environment, from which we deduce a lifetime of ~17 ps for non-equilibrium populations.
@article{arxiv.2108.00989,
title = {Phase-dependent microwave response of a graphene Josephson junction},
author = {Roy Haller and Gergő Fülöp and David Indolese and Joost Ridderbos and Rainer Kraft and Luk Yi Cheung and Jann Hinnerk Ungerer and Kenji Watanabe and Takashi Taniguchi and Detlef Beckmann and Romain Danneau and Pauli Virtanen and Christian Schönenberger},
journal= {arXiv preprint arXiv:2108.00989},
year = {2022}
}