Interplay between kinetic inductance, non-linearity and quasiparticle dynamics in granular aluminum MKIDs

Microwave kinetic inductance detectors (MKIDs) are thin film, cryogenic, superconducting resonators. Incident Cooper pair-breaking radiation increases their kinetic inductance, thereby measurably lowering their resonant frequency. For a given resonant frequency, the highest MKID responsivity is obtained by maximizing the kinetic inductance fraction $\alpha$. However, in circuits with $\alpha$ close to unity, the low supercurrent density reduces the maximum number of readout photons before bifurcation due to self-Kerr non-linearity, therefore setting a bound for the maximum $\alpha$ before the noise equivalent power (NEP) starts to increase. By fabricating granular aluminum MKIDs with different resistivities, we effectively sweep their kinetic inductance from tens to several hundreds of pH per square. We find a NEP minimum in the range of $25\; \text{aW}/\sqrt{\text{Hz}}$ at $\alpha \approx 0.9$, which results from a tradeoff between the onset of non-linearity and a non-monotonic dependence of the noise spectral density vs. resistivity.