Energy relaxation properties of a microwave resonator coupled to a pumped two-level system bath

While the main loss channel of planar microwave superconducting resonators has been identified to be related to an external coupling to a two-level system bath, the behavior of such a cavity in an environment strongly pumped by a detuned tone has yet to be fully understood. Here, a semi-classical theoretical model describing the interaction of such resonators with the Two-Level Systems is derived, to which experimental datas obtained with different substrate materials are fitted. Performing the experiments with different substrates allows the tailoring of fundamental properties of the interacting two-level system bath.