Modelling dielectric loss in superconducting resonators: Evidence for interacting atomic two-level systems at the Nb/oxide interface

While several experiments claim that two-level system (TLS) defects in amorphous surfaces/interfaces are responsible for energy relaxation in superconducting resonators and qubits, none can provide quantitative explanation of their data in terms of the conventional noninteracting TLS model. Here a model that interpolates between the interacting and noninteracting TLS loss tangent is proposed to perform numerical analysis of experimental data and extract information about TLS parameters and their distribution. As a proof of principle, the model is applied to TESLA cavities that contain only a single lossy material in their interior, the niobium/niobium oxide interface. The best fits show interacting TLSs with a sharp modulus of electric dipole moment for both thin (5 nm) and thick (100 nm) oxides, indicating that the TLSs are "atomic" instead of "glassy". The proposed method can be applied to other devices with multiple material interfaces and substrates, with the goal of elucidating the nature of TLSs causing energy loss in resonators and qubits.