Granular aluminum kinetic inductance nonlinearity

Granular Aluminum is a superconductor known for more than eighty years, which recently found its application in qubits, microwave detectors and compact resonators, due to its high kinetic inductance, critical magnetic field and critical current. Here we report on the nonlinear dependence of granular Aluminum inductance on current, which hints towards parametric amplification of the microwave signal in granular Aluminum films. The phase shift of the microwave signal reached $4$ rad at a frequency of $7$ GHz, which makes it possible to estimate the nonlinearity of the system as $\Delta \phi {\text{/}}\phi = 1.4\% $ and the potential gain of the order of $17$ dB.