Linear and Nonlinear Properties of a Compact High-Kinetic-Inductance WSi Multimode Resonator

The kinetic inductance (KI) of superconducting devices can be exploited for reducing the footprint of linear elements as well as for introducing nonlinearity to the circuit. We characterize the linear and nonlinear properties of a multimode resonator fabricated from amorphous tungsten silicide (WSi) with a fundamental frequency of ($f_1 = 172$) MHz. We show how the multimode structure of the device can be used to extract the different quality factors and to aid the nonlinear characterization. In the linear regime the footprint is reduced by a factor of $\sim 0.35$ with standard lateral dimensions with no significant degradation of the quality factor compared to a similar Al device . In the nonlinear regime we observe self positive frequency shifts at low powers which can be attributed to heating of tunneling two-level systems. The cross mode nonlinearities are described well by a Kerr model with a self-Kerr coefficient in the order of $|K_{11}|/2\pi \approx 1.5\times10^{-7}$ Hz/photon. These properties together with a reproducible fabrication process make WSi a promising candidate for creating linear and nonlinear circuit QED elements.