Granular aluminum: A source of non-linearity for superconducting quantum circuits

Superconducting granular aluminum (grAl) has already proven its applicability as linear inductor in kinetic inductance detectors and Fluxonium qubit designs [1]. Evaporated in an oxygen atmosphere, aluminum self-assembles into crystalline grains separated by amorphous aluminum oxide, resulting in highly inductive and low-loss superconducting grAl films [2]. We model the cQED properties of grAl microwave resonators using an effective array of Josephson junctions, and obtain self-Kerr coefficients that are inversely proportional to the grAl volume and the critical current density [3]. By shunting a small grAl volume with a thin film aluminum capacitor, we enhance the self-Kerr nonlinearity of the resulting LC mode, K₁₁, up to values much larger than the spectral linewidth of the fundamental mode, κ, with K₁₁ ≈ 100×κ. By driving the resonator with increasingly larger power, we observe up to 30 multi-photon transitions between the levels of the fundamental mode, from which we extract a value of K₁₁ in the MHz range.

[1] Grünhaupt, Spiecker, et al. arXiv:1809.10646
[2] Grünhaupt et al. Phys. Rev. Lett., 121, 117001 (2018)
[3] Maleeva et al. Nature Comm., 9, 3889 (2018)