We have measured the dielectric response of amorphous insulators in the audio frequency range at temperatures between 500 μK and 400 mK. We compare the measured superlinear behavior with a model incorporating higher order terms at low frequencies. Temperature independent dielectric response at low fields and low temperatures has also been observed which may indicate a low energy cutoff in the two-level system distribution of order 1 mK in some materials. We also find anomalously high sensitivity of the dielectric response to rf noise.

DOI:https://doi.org/10.1103/PhysRevB.55.11256