Probing a two-level system bath via the frequency shift of an off-resonantly-driven cavity

TL;DR

This paper introduces a semi-classical model to understand how an off-resonant pump affects the frequency and damping of microwave resonators coupled to a two-level system bath, validated through experiments.

Contribution

It presents a new semi-classical model predicting power-dependent frequency shifts in resonators influenced by TLS baths, validated by experimental two-tone spectroscopy.

Findings

Model accurately predicts frequency shifts due to TLS bath

Experimental validation across various substrates

Provides a tool to characterize TLS properties

Abstract

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.