Circuit-QED with phase-biased Josephson weak links

TL;DR

This paper develops a theoretical framework to understand how the occupancy of Andreev states in superconducting weak links affects the response of a coupled microwave resonator, aiding interpretation of circuit-QED experiments.

Contribution

It introduces a formalism combining Bogoliubov-de Gennes theory with resonator coupling to quantitatively analyze Andreev state effects in circuit-QED systems.

Findings

Calculated resonator frequency shifts due to Andreev level occupancy.

Described how microwave drives induce transitions between Andreev states.

Applied the model to interpret recent experimental data.

Abstract

By coupling a superconducting weak link to a microwave resonator, recent experiments probed the spectrum and achieved the quantum manipulation of Andreev states in various systems. However, the quantitative understanding of the response of the resonator to changes in the occupancy of the Andreev levels, which are of fermionic nature, is missing. Here, using Bogoliubov-de Gennes formalism to describe the weak link and a general formulation of the coupling to the resonator, we calculate the shift of the resonator frequency as a function of the levels occupancy and describe how transitions are induced by phase or electric field microwave drives. We apply this formalism to analyze recent experimental results obtained using circuit-QED techniques on superconducting atomic contacts and semiconducting nanowire Josephson junctions.