Microwave spectroscopy of Schmid transition

TL;DR

This paper predicts the frequency-dependent admittance and reflection phase shift in quantum circuits with Josephson junctions, providing a way to identify the Schmid transition through finite-frequency measurements.

Contribution

It offers a theoretical framework for understanding the frequency response of various quantum circuits near the Schmid transition, aiding experimental identification.

Findings

Frequency dependence of admittance and reflection phase shift predicted

Universal scaling of responses with frequency identified

Guidelines for experimental detection of Schmid transition provided

Abstract

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.