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

Understand

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.