Thin film high quality superconductor microresonators are important for a number of diverse applications that range from quantum computation to submillimeter and far-infrared astronomy. The performance of these devices has improved dramatically over the past decades and resonator quality factors above 106 are now routinely achieved using single-layer structures deposited on high-quality low-loss crystalline substrate. Achieving high-quality factors requires minimizing all potential sources of dissipation and noise. One prominent source of dissipation in microresonators has been found to be Two Level Systems (TLSs) in thin amorphous dielectric surface layers of the microresonators. These TLS are also responsible for an excess frequency noise in the resonators. A microscopic theory for TLSs noise frequency in microresonators is not yet available.
In this talk we shall first review data of recent experiments performed on high quality superconducting microresonator where low frequency noise spectra have been studied in varying temperature and applied power. We shall show that the data are inconsistent with the Standard Tunneling Model (STM) for TLS in amorphous dielectrics. We shall then propose a new model, the Generalized Tunneling Model (GTM) which includes strong interactions between TLS and a slow power law dependence of their density of states. We show that the predictions of this model are in a perfect agreement with the recent studies of the noise in high quality superconducting resonators. The predictions also agree with the temperature dependence of the TLS dephasing rates observed in phase qubits. Finally, we discuss the origin of the universal dimensionless parameter that controls the interaction between TLS in glasses and show that it is consistent with the assumptions of the GTM.