Anomalous positive non-linearity in superconducting granular aluminum resonators

Superconducting high-kinetic inductance materials like granular aluminum (grAl) are a versatile part of the cQED toolbox enabling the implementation of low-loss and compact inductors. For microwave resonators built from these materials, the Kerr coefficient associated with the superconducting condensate is typically negative. In this talk, we report an anomalous positive Kerr non-linearity observed in grAl resonators, which manifests as a positive frequency shift with increasing readout power. Interestingly, at higher temperatures the Kerr coefficient sign reverses to negative, revealing a corresponding energy scale which depends on the normal-state resistivity of the grAl film. A similar effect occurs with the increase of microwave power. The time dynamics after high energy events in these resonators also show an anomalous frequency response with longer relaxation time scales. We find that changes in frequency shift and quality factor with power and temperature, taken together, cannot be explained with a typical two-level-system (TLS) model.