Circuit quantum electrodynamics of granular Aluminum resonators

Granular Aluminum (GrAl) thin film structures can be used as superinductors in superconducting qubits, or as high kinetic inductance detectors for mm wavelength radiation. Their microstructure consists of pure Aluminum grains of 2-5 nm diameter, separated by thin aluminum oxide barriers, forming a self-assembled network of Josephson junctions. We model microwave resonators made of GrAl as a 1D array of effective Josephson junctions, directly relating their dispersion relation and nonlinearity to GrAl microstructure. Below 20 GHz, we can measure the dispersion relation of GrAl stripline resonators using a circuit quantum electrodynamics (cQED) setup. We observe self-Kerr coefficients in the range of 1-100 Hz/photon, depending on the resonator geometry and the sheet resistance of the film. Using an optical setup designed for mm wave spectroscopy we measure the plasma frequency of the film around 75 GHz. These results are in agreement with values calculated using our effective Josephson junction chain model, and they are encouraging for the design of cQED elements such as qubits or parametric amplifiers using GrAl.