High Impedance Granular Aluminum Ring Resonators

Superconducting inductors with impedance surpassing the resistance quantum, i.e., superinductors, are important for quantum technologies because they enable the development of protected qubits, enhance coupling to systems with small electric dipole moments, and facilitate the study of phase-slip physics. We demonstrate superinductors with densely packed meandered traces of granular aluminum (grAl) with inductances up to $4\,\mu\mathrm{H}$, achieving impedances exceeding $100\,\mathrm{k}\Omega$ in the $4-8\,\mathrm{GHz}$ range. Ring resonators made with grAl meandered superinductors exhibit quality factors on the order of $10^5$ in the single-photon regime and low non-linearity on the order of tens of $\mathrm{Hz}$. Depending on the grAl resistivity, at $10\,\mathrm{Hz}$, we measure frequency noise spectral densities in the range of $10^2$ to $10^3\,\mathrm{Hz}/\sqrt{\mathrm{Hz}}$. In some devices, in the single-photon regime, we observe a positive Kerr coefficient of unknown origin. Using more complex fabrication, the devices could be released from the substrate, either freestanding or suspended on a membrane, thereby further improving their impedance by a factor of three.