High kinetic inductance NbTiN superconducting transmission line resonators in the very thin film limit

We examine the DC and radio frequency (RF) response of superconducting transmission line resonators comprised of very thin NbTiN films, < 12 nm in thickness, in the high-temperature limit, where the photon energy is less than the thermal energy. The resonant frequencies of these superconducting resonators show a significant nonlinear response as a function of RF input power, which can approach a frequency shift of Δ f = - 0.15 % in a - 20 dB span in the thinnest film. The strong nonlinear response allows these very thin film resonators to serve as high kinetic inductance parametric amplifiers.