Evidence for universal relationship between the measured 1/f permittivity noise and loss tangent created by tunneling atoms

Noise from atomic tunneling systems (TSs) limit the performance of various resonant devices, ranging in application from astronomy detectors to quantum computing. Using devices containing these TSs, we study the $1/f$ permittivity noise and loss tangent in two film types containing different TS densities. The noise reveals an intrinsic value as well as the crossover to power-saturated noise. The intrinsic $1/f$ noise fits to the temperature dependence $1/T^{1+\mu}$ where $0.2\le\mu\le0.7$, which is related to previous studies and strongly interacting TS. An analysis of the noise normalized by the loss tangent and temperature is quantitatively identical for two film types, despite a factor of 5 difference in their loss tangent. Following from the broad applicability of the TS model, the data supports a universal relationship for amorphous-solid produced permittivity noise. The quantity of the observed noise particularly supports a recent model in which noise is created by weak TS-TS interactions.