Although the main loss channel of planar microwave superconducting resonators has been identified to be related to an external coupling to a two-level system (TLS) bath, the behavior of such a cavity in the presence of an off-resonant pump has yet to be fully understood. Here a semi-classical model that predicts a power-dependent frequency shift besides the well-known TLS-induced damping is derived. The model is validated experimentally by performing a two-tone spectroscopy of several resonators fabricated on various substrates. Together with the provided analytic formulas, the technique proposed here is a simple, yet powerful, tool to characterize various properties of the TLS bath, such as their average dephasing rate.
@article{arxiv.1805.04397,
title = {Probing a two-level system bath via the frequency shift of an off-resonantly-driven cavity},
author = {Thibault Capelle and Emmanuel Flurin and Edouard Ivanov and Jose Palomo and Michael Rosticher and Sheon Chua and Tristan Briant and Pierre-François Cohadon and Antoine Heidmann and Thibaut Jacqmin and Samuel Deleglise},
journal= {arXiv preprint arXiv:1805.04397},
year = {2020}
}