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 (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>grAl</a:mi></a:math>) with inductances up to 4 µH, achieving impedances exceeding 100 k in the 4–8 GHz range. Ring resonators made with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>grAl</c:mi></c:math> meandered superinductors exhibit quality factors on the order of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mn>10</e:mn><e:mn>5</e:mn></e:msup></e:math> in the single-photon regime, and low nonlinearity on the order of tens of hertz. Depending on the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>grAl</g:mi></g:math> resistivity, at 10 Hz, we measure frequency-noise spectral densities in the range of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mn>10</i:mn><i:mn>2</i:mn></i:msup></i:math>–<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mn>10</k:mn><k:mn>3</k:mn></k:msup><k:mspace width="0.2em"/><k:mi>Hz</k:mi><k:mo>/</k:mo><k:mrow><k:msqrt><k:mi>Hz</k:mi></k:msqrt></k:mrow></k:math>. 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 3.