Non-linear Hybrid Microwave Resonators Made by He-Beam Assisted Deposition of Tungsten Nanowires

We evaluate the performance of hybrid microwave resonators made by combining sputtered Nb thin films with Tungsten nanowires grown with a He-beam induced deposition technique. Depending on growth conditions the nanowires have a typical width $w\in[35-75]$~nm and thickness $t\in[5-40]$~nm. We observe a high normal state resistance $R_{sq}\in [65-150]$ $\Omega/sq$ which together with a critical temperature $T_c\in[4-6]~K$ ensure a high kinetic inductance fraction making the resonator strongly nonlinear. Both lumped and coplanar waveguide resonators were fabricated and measured at low temperature exhibiting internal quality factors up to $3990$ at $4.5$~GHz in the few photon regime. Analyzing the wire length, temperature and microwave power dependence we extracted a kinetic inductance for the W nanowire of $L_K\approx15$ pH/$sq$, a kinetic inductance fraction $\alpha_{W,He}=0.996$ and a Kerr non-linearity as high as $K_{W,He}/2\pi=164$~Hz/photon at $4.5$~GHz. This study allows us to conclude that the nanowires made with the helium focused ion beam are very versatile objects to engineer compact, high impedance, superconducting environments.