Schmid transition was introduced first as a superconductor-insulator transition in the zero-frequency response of a shunted Josephson junction in equilibrium at zero temperature. As it is typical for a quantum impurity problem, at finite frequencies the transition is broadened to a crossover. Modern attempts to find Schmid transition rely on finite-frequency measurements of a quantum circuit. We predict the frequency dependence of the admittance and reflection phase shift for a high-impedance transmission line terminated by a Josephson junction for a wide variety of devices, from a charge qubit to a transmon. Our results identify the circuit parameters allowing for the universal scaling of the responses with frequency, thus helping to identify the Schmid transition from the finite-frequency measurements.
@article{arxiv.2308.16072,
title = {Microwave spectroscopy of Schmid transition},
author = {Manuel Houzet and Tsuyoshi Yamamoto and Leonid I. Glazman},
journal= {arXiv preprint arXiv:2308.16072},
year = {2023}
}