Power and temperature dependence of High Q superconducting resonators

Loss measurements of high-quality factor superconducting resonators are often performed to assess microwave loss resulting from two-level system (TLS) defects. Unfortunately, power dependent loss measurements are unable to isolate loss resulting from quasiparticles or other sources. However, temperature and power dependent resonator measurements of the loss and fractional frequency shift provide greater insight.

An integrated model that combines an interacting TLS model and nonequilibrium quasiparticles is used to describe data from TiN and Al resonators that experience effects from both TLS defects and quasiparticles. Data is collected in an adiabatic demagnetization refrigerator with magnetic shielding, light-tight boxes, and line filtering that is insufficient to completely isolate the measure devices from its environment. This model is sufficient to describe the loss and frequency shift from 50 mK to 1 K for TiN (or 300 mK for Al), temperatures sufficient for thermal quasiparticles to dominate the behavior, and average photon numbers ranging from 1 to 1M. For these resonators that exhibit quality factors over 1M, some insight into TLS-TLS interactions may be possible.