Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2503.13321 · Physical Review Applied

Magnetic-field-resilient high-impedance high-kinetic-inductance superconducting resonators

C. Roy, S. Frasca, Pasquale Scarlino

Published Dec 17, 2025• 2 citations
arXivHTMLPDF

Abstract

Superconducting resonators with high-kinetic inductance play a central role in hybrid quantum circuits, enabling strong coupling with quantum systems with small electric dipole moment and improved parametric amplification. However, optimizing these resonators simultaneously for high internal quality factors ($Q_i$) and resilience to strong magnetic fields remains challenging. In this study, we systematically compare superconducting resonators fabricated from niobium nitride (NbN) and granular aluminum (grAl) thin films, each having similar kinetic inductance values ($L_k \sim 100$ pH/sq). At zero magnetic field, resonators made from grAl exhibit higher $Q_i$ compared to their NbN counterparts. However, under applied magnetic fields, NbN resonators demonstrate significantly better resilience. Moreover, NbN resonators exhibit an unexpected increase in $Q_i$ at intermediate in-plane magnetic fields ($B_{\parallel} \sim 1$ T), which we attribute to an enhanced frequency detuning that reduce coupling to two-level system defects. In contrast, grAl resonators show a distinct critical field above which $Q_i$ rapidly decreases, strongly depending on resonator cross-section respect to the applied field direction. Characterization of the nonlinear properties at zero magnetic field reveals that the self-Kerr coefficient in grAl resonators is more than an order of magnitude higher than in NbN resonators, making grAl particularly attractive for applications requiring pronounced nonlinear interactions. Our findings illustrate a clear trade-off between the two materials: NbN offers superior magnetic-field resilience beneficial for hybrid circuit quantum electrodynamics applications, while grAl is more advantageous in low-field regimes demanding high impedance and strong nonlinearity.

DOI
10.1103/76rr-lx9l

Related papers

Magnetic field resilient high kinetic inductance superconducting niobium nitride coplanar waveguide resonators

Cécile Xinqing Yu, Simon Zihlmann, Gonzalo Troncoso Fernández-Bada +4 more

We characterize niobium nitride (NbN) λ/2 coplanar waveguide resonators, which were fabricated from a 10-nm-thick film on silicon dioxide grown by sputter deposition. For films grown at 180 °C, we report a superconducting critical temperature of 7.4 K associated with a normal square resistance of 1 kΩ, leading to a kinetic inductance of 192 pH/◻. We fabricated resonators with a characteristic impedance up to 4.1 kΩ and internal quality factors Qi>104 in the single photon regime at zero magnetic field. Moreover, in the many photon regime, the resonators present a high magnetic field resilience with Qi>104 in a 6 T in-plane magnetic field and in a 300 mT out-of-plane magnetic field. These findings make such resonators a compelling choice for circuit quantum electrodynamics experiments involving quantum systems with small electric dipole moments operated in finite magnetic fields.

arXiv:2012.04366•Applied Physics Letters•Feb 1, 2021•59 citations

Superconducting granular aluminum resonators resilient to magnetic fields up to 1 Tesla

Kiril Borisov, D. Rieger, Patrick Winkel +8 more

High kinetic inductance materials constitute a valuable resource for superconducting quantum circuits and hybrid architectures. Superconducting granular aluminum (grAl) reaches kinetic sheet inductances in the nH/□ range, with proven applicability in superconducting quantum bits and microwave detectors. Here, we show that the single photon internal quality factor Qi of grAl microwave resonators exceeds 105 in magnetic fields up to 1 T, aligned in-plane to the grAl films. Small perpendicular magnetic fields, in the range of 0.5 mT, enhance Qi by approximately 15%, possibly due to the introduction of quasiparticle traps in the form of fluxons. Further increasing the perpendicular field deteriorates the resonators' quality factor. These results open the door for the use of high kinetic inductance grAl structures in circuit quantum electrodynamics and hybrid architectures with magnetic field requirements.

arXiv:2006.05171•Applied Physics Letters•Sep 21, 2020•49 citations

Pushing the Boundaries of Impedance and Nonlinearity in Superconducting Quantum Circuits Based on Granular Aluminum

Mahya Khorramshahi

Superconducting circuits based on high kinetic inductance materials are promising candidates for future quantum technologies, owing to their magnetic field resilience, low microwave losses, and lithographic scalability. In this thesis, we explore the properties of granular aluminum (grAl) resonators in two distinct geometries, using the nonlinear kinetic inductance of grAl for applications in superconducting quantum circuits. In the first part, we present compact meandered ring resonators fabricated using a single-step electron-beam lithography and lift-off process. By optimizing film resistivity and geometry, we achieve superinductors with characteristic impedances exceeding \(100~\mathrm{k}\Omega\), corresponding to total inductances of several microhenries, while maintaining internal quality factors on the order of \(10^{5}\) in the single-photon regime. In the second part, we investigate DC-tunable resonators based on a \(3\lambda/4\) fractal geometry that allows direct current injection for in-situ tuning of the resonance frequency. We achieve frequency tunability up to \(4.5\%\) and analyze the nonlinear kinetic inductance using models based on Ginzburg-Landau, Mattis-Bardeen-BCS, and an effective Josephson-junction-array model. This work establishes granular aluminum as a material for realizing high-impedance and frequency-tunable superconducting circuits, offering new opportunities for advanced applications in protected qubits, hybrid quantum systems, broadband phase shifters, and three-wave mixing parametric amplifiers.

•Jan 1, 2026•0 citations

NbN films with high kinetic inductance for high-quality compact superconducting resonators

Simone Frasca, Ivo Arabadzhiev, Sebastien Yves Bros de Puechredon +7 more

Niobium nitride ($\mathrm{Nb}\mathrm{N}$) is a particularly promising material for quantum technology applications, as it shows the degree of reproducibility necessary for large-scale superconducting circuits. We demonstrate that resonators based on $\mathrm{Nb}\mathrm{N}$ thin films present a one-photon internal quality factor above ${10}^{5}$ maintaining a high impedance (larger than $2\mathrm{k}\mathrm{\ensuremath{\Omega}}$), with a footprint of approximately $50\ifmmode\times\else\texttimes\fi{}100\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ and a Kerr nonlinearity of few tenths of a hertz. These quality factors, mostly limited by losses induced by the coupling to two-level systems, have been maintained for kinetic inductances ranging from tenths to hundreds of picoHenry per square. We also demonstrate minimal variations in the performance of the resonators during multiple cooldowns over more than nine months. Our work proves the versatility of niobium nitride high-kinetic-inductance resonators, opening perspectives towards the fabrication of compact, high-impedance, and high-quality multimode circuits, with sizable interactions.

arXiv:2302.13930•Physical Review Applied•Oct 9, 2023•37 citations

High-impedance granular-aluminum ring resonators

Mahya Khorramshahi, Martin Spiecker, Patrick Paluch +10 more

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 ( grAl ) with inductances up to 4 µH, achieving impedances exceeding 100 k in the 4–8 GHz range. Ring resonators made with grAl meandered superinductors exhibit quality factors on the order of 10 5 in the single-photon regime, and low nonlinearity on the order of tens of hertz. Depending on the grAl resistivity, at 10 Hz, we measure frequency-noise spectral densities in the range of 10 2 – 10 3 Hz / Hz . 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.

arXiv:2506.07761•Physical Review Applied•Jul 14, 2025•2 citations

Low-loss lumped-element inductors made from granular aluminum

Vishakha Gupta, Patrick Winkel, Neel Thakur +5 more

Lumped-element inductors are an integral component in the circuit QED toolbox. However, it is challenging to build inductors that are simultaneously compact, linear, and low-loss with standard approaches that either rely on the geometric inductance of superconducting thin films or on the kinetic inductance of Josephson-junction arrays. In this work, we overcome this challenge by utilizing the high kinetic inductance offered by superconducting granular aluminum (grAl). We demonstrate lumped-element inductors with a few nH of inductance that are up to 100 times shorter than inductors built from pure aluminum (Al). To characterize the properties of these linear inductors, we first report on the performance of lumped-element resonators built entirely out of grAl with sheet inductances varying from 30 – 320 pH/sq and self-Kerr nonlinearities of 0.2 – 20 Hz / photon . Further, we demonstrate integration of these grAl inductors into hybrid resonators with Al or tantalum ( Ta ) capacitor electrodes without increasing total internal losses. Interestingly, the measured internal quality factors systematically decrease with increasing room-temperature resistivity of the grAl film for all devices, indicating a trade-off between compactness and internal loss. For our lowest resistivity grAl films, we measure quality factors reaching 3.5 × 10 6 for the all-grAl devices and 4.5 × 10 6 for the hybrid grAl/ Ta devices, similar to state-of-the-art quantum circuits. Our loss analysis suggests that the surface-loss factor of grAl is similar to that of pure Al for our lowest resistivity films, while the increasing losses with resistivity could be explained by increasing inductor loss in the grAl film.

arXiv:2411.12611•Physical Review Applied•May 27, 2025•14 citations
Superconducting resonators with high-kinetic inductance play a central role in hybrid quantum circuits, enabling strong coupling with quantum systems with small electric dipole moment and improved parametric amplification. However, optimizing these resonators simultaneously for high internal quality factors (QiQ_iQi​) and resilience to strong magnetic fields remains challenging. In this study, we systematically compare superconducting resonators fabricated from niobium nitride (NbN) and granular aluminum (grAl) thin films, each having similar kinetic inductance values (Lk∼100L_k \sim 100Lk​∼100 pH/sq). At zero magnetic field, resonators made from grAl exhibit higher QiQ_iQi​ compared to their NbN counterparts. However, under applied magnetic fields, NbN resonators demonstrate significantly better resilience. Moreover, NbN resonators exhibit an unexpected increase in QiQ_iQi​ at intermediate in-plane magnetic fields (B∥∼1B_{\parallel} \sim 1B∥​∼1 T), which we attribute to an enhanced frequency detuning that reduce coupling to two-level system defects. In contrast, grAl resonators show a distinct critical field above which QiQ_iQi​ rapidly decreases, strongly depending on resonator cross-section respect to the applied field direction. Characterization of the nonlinear properties at zero magnetic field reveals that the self-Kerr coefficient in grAl resonators is more than an order of magnitude higher than in NbN resonators, making grAl particularly attractive for applications requiring pronounced nonlinear interactions. Our findings illustrate a clear trade-off between the two materials: NbN offers superior magnetic-field resilience beneficial for hybrid circuit quantum electrodynamics applications, while grAl is more advantageous in low-field regimes demanding high impedance and strong nonlinearity.
We characterize niobium nitride (NbN) λ/2 coplanar waveguide resonators, which were fabricated from a 10-nm-thick film on silicon dioxide grown by sputter deposition. For films grown at 180 °C, we report a superconducting critical temperature of 7.4 K associated with a normal square resistance of 1 kΩ, leading to a kinetic inductance of 192 pH/◻. We fabricated resonators with a characteristic impedance up to 4.1 kΩ and internal quality factors Qi>104 in the single photon regime at zero magnetic field. Moreover, in the many photon regime, the resonators present a high magnetic field resilience with Qi>104 in a 6 T in-plane magnetic field and in a 300 mT out-of-plane magnetic field. These findings make such resonators a compelling choice for circuit quantum electrodynamics experiments involving quantum systems with small electric dipole moments operated in finite magnetic fields.
High kinetic inductance materials constitute a valuable resource for superconducting quantum circuits and hybrid architectures. Superconducting granular aluminum (grAl) reaches kinetic sheet inductances in the nH/□ range, with proven applicability in superconducting quantum bits and microwave detectors. Here, we show that the single photon internal quality factor Qi of grAl microwave resonators exceeds 105 in magnetic fields up to 1 T, aligned in-plane to the grAl films. Small perpendicular magnetic fields, in the range of 0.5 mT, enhance Qi by approximately 15%, possibly due to the introduction of quasiparticle traps in the form of fluxons. Further increasing the perpendicular field deteriorates the resonators' quality factor. These results open the door for the use of high kinetic inductance grAl structures in circuit quantum electrodynamics and hybrid architectures with magnetic field requirements.
Superconducting circuits based on high kinetic inductance materials are promising candidates for future quantum technologies, owing to their magnetic field resilience, low microwave losses, and lithographic scalability. In this thesis, we explore the properties of granular aluminum (grAl) resonators in two distinct geometries, using the nonlinear kinetic inductance of grAl for applications in superconducting quantum circuits. In the first part, we present compact meandered ring resonators fabricated using a single-step electron-beam lithography and lift-off process. By optimizing film resistivity and geometry, we achieve superinductors with characteristic impedances exceeding 100 kΩ100~\mathrm{k}\Omega100 kΩ, corresponding to total inductances of several microhenries, while maintaining internal quality factors on the order of 10510^{5}105 in the single-photon regime. In the second part, we investigate DC-tunable resonators based on a 3λ/43\lambda/43λ/4 fractal geometry that allows direct current injection for in-situ tuning of the resonance frequency. We achieve frequency tunability up to 4.5%4.5\%4.5% and analyze the nonlinear kinetic inductance using models based on Ginzburg-Landau, Mattis-Bardeen-BCS, and an effective Josephson-junction-array model. This work establishes granular aluminum as a material for realizing high-impedance and frequency-tunable superconducting circuits, offering new opportunities for advanced applications in protected qubits, hybrid quantum systems, broadband phase shifters, and three-wave mixing parametric amplifiers.
Niobium nitride (NbN\mathrm{Nb}\mathrm{N}NbN) is a particularly promising material for quantum technology applications, as it shows the degree of reproducibility necessary for large-scale superconducting circuits. We demonstrate that resonators based on NbN\mathrm{Nb}\mathrm{N}NbN thin films present a one-photon internal quality factor above 105{10}^{5}105 maintaining a high impedance (larger than $2\mathrm{k}\mathrm{\ensuremath{\Omega}}$), with a footprint of approximately $50\ifmmode\times\else\texttimes\fi{}100\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ and a Kerr nonlinearity of few tenths of a hertz. These quality factors, mostly limited by losses induced by the coupling to two-level systems, have been maintained for kinetic inductances ranging from tenths to hundreds of picoHenry per square. We also demonstrate minimal variations in the performance of the resonators during multiple cooldowns over more than nine months. Our work proves the versatility of niobium nitride high-kinetic-inductance resonators, opening perspectives towards the fabrication of compact, high-impedance, and high-quality multimode circuits, with sizable interactions.
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 ( grAl ) with inductances up to 4 µH, achieving impedances exceeding 100 k in the 4–8 GHz range. Ring resonators made with grAl meandered superinductors exhibit quality factors on the order of 10 5 in the single-photon regime, and low nonlinearity on the order of tens of hertz. Depending on the grAl resistivity, at 10 Hz, we measure frequency-noise spectral densities in the range of 10 2 – 10 3 Hz / Hz . 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.
Lumped-element inductors are an integral component in the circuit QED toolbox. However, it is challenging to build inductors that are simultaneously compact, linear, and low-loss with standard approaches that either rely on the geometric inductance of superconducting thin films or on the kinetic inductance of Josephson-junction arrays. In this work, we overcome this challenge by utilizing the high kinetic inductance offered by superconducting granular aluminum (grAl). We demonstrate lumped-element inductors with a few nH of inductance that are up to 100 times shorter than inductors built from pure aluminum (Al). To characterize the properties of these linear inductors, we first report on the performance of lumped-element resonators built entirely out of grAl with sheet inductances varying from 30 – 320 pH/sq and self-Kerr nonlinearities of 0.2 – 20 Hz / photon . Further, we demonstrate integration of these grAl inductors into hybrid resonators with Al or tantalum ( Ta ) capacitor electrodes without increasing total internal losses. Interestingly, the measured internal quality factors systematically decrease with increasing room-temperature resistivity of the grAl film for all devices, indicating a trade-off between compactness and internal loss. For our lowest resistivity grAl films, we measure quality factors reaching 3.5 × 10 6 for the all-grAl devices and 4.5 × 10 6 for the hybrid grAl/ Ta devices, similar to state-of-the-art quantum circuits. Our loss analysis suggests that the surface-loss factor of grAl is similar to that of pure Al for our lowest resistivity films, while the increasing losses with resistivity could be explained by increasing inductor loss in the grAl film.