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High-impedance granular-aluminum ring resonators

Mahya Khorramshahi1,*, Martin Spiecker1,2, Patrick Paluch1,2, Simon Geisert1, Nicolas Gosling1, Nicolas Zapata1, Lucas Brauch1, Christian Kübel3,4,5, Simone Dehm3 et al.

Ralph Krupke1,3, Wolfgang Wernsdorfer1,2, Ioan M. Pop1,2,6, and Thomas Reisinger1,†

  • *Contact author: mahya.khorramshahi@kit.edu
  • †Contact author: thomas.reisinger@kit.edu

Phys. Rev. Applied 24, 024066 – Published 27 August, 2025

DOI: https://doi.org/10.1103/n73t-7q1n

Abstract

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 kΩ in the 4–8 GHz range. Ring resonators made with grAl meandered superinductors exhibit quality factors on the order of 105 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 102–103Hz/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.

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References (71)

  1. M. Devoret, S. Girvin, and R. Schoelkopf, Circuit-QED: How strong can the coupling between a Josephson junction atom and a transmission line resonator be? Ann. Phys. 519, 767 (2007).
  2. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  3. P. Arrangoiz-Arriola, E. A. Wollack, M. Pechal, J. D. Witmer, J. T. Hill, and A. H. Safavi-Naeini, Coupling a superconducting quantum circuit to a phononic crystal defect cavity, Phys. Rev. X 8, 031007 (2018).
  4. A. Bozkurt, H. Zhao, C. Joshi, H. G. LeDuc, P. K. Day, and M. Mirhosseini, A quantum electromechanical interface for long-lived phonons, Nat. Phys. 19, 1326 (2023).
  5. A. André, D. DeMille, J. M. Doyle, M. D. Lukin, S. E. Maxwell, P. Rabl, R. J. Schoelkopf, and P. Zoller, A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators, Nat. Phys. 2, 636 (2006).
  6. V. E. Manucharyan, N. A. Masluk, A. Kamal, J. Koch, L. I. Glazman, and M. H. Devoret, Evidence for coherent quantum phase slips across a Josephson junction array, Phys. Rev. B 85, 024521 (2012).
  7. N. A. Masluk, I. M. Pop, A. Kamal, Z. K. Minev, and M. H. Devoret, Microwave characterization of Josephson junction arrays: Implementing a low loss superinductance, Phys. Rev. Lett. 109, 137002 (2012).
  8. V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single Cooper-pair circuit free of charge offsets, Science 326, 113 (2009).
  9. I. M. Pop, K. Geerlings, G. Catelani, R. J. Schoelkopf, L. I. Glazman, and M. H. Devoret, Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles, Nature 508, 369 (2014).
  10. L. Grünhaupt, M. Spiecker, D. Gusenkova, N. Maleeva, S. T. Skacel, I. Takmakov, F. Valenti, P. Winkel, H. Rotzinger, W. Wernsdorfer, A. V. Ustinov, and I. M. Pop, Granular aluminium as a superconducting material for high-impedance quantum circuits, Nat. Mater. 18, 816 (2019).
  11. M. Pita-Vidal, A. Bargerbos, C.-K. Yang, D. J. Van Woerkom, W. Pfaff, N. Haider, P. Krogstrup, L. P. Kouwenhoven, G. De Lange, and A. Kou, Gate-tunable field-compatible fluxonium, Phys. Rev. Appl. 14, 064038 (2020).
  12. L. B. Nguyen, G. Koolstra, Y. Kim, A. Morvan, T. Chistolini, S. Singh, K. N. Nesterov, C. Jünger, L. Chen, Z. Pedramrazi, B. K. Mitchell, J. M. Kreikebaum, S. Puri, D. I. Santiago, and I. Siddiqi, Blueprint for a high-performance fluxonium quantum processor, PRX Quantum 3, 037001 (2022).
  13. M. Peruzzo, F. Hassani, G. Szep, A. Trioni, E. Redchenko, M. Žemlička, and J. M. Fink, Geometric superinductance qubits: Controlling phase delocalization across a single Josephson junction, PRX Quantum 2, 040341 (2021).
  14. K. Kalashnikov, W. T. Hsieh, W. Zhang, W.-S. Lu, P. Kamenov, A. Di Paolo, A. Blais, M. E. Gershenson, and M. Bell, Bifluxon: Fluxon-parity-protected superconducting qubit, PRX Quantum 1, 010307 (2020).
  15. P. Brooks, A. Kitaev, and J. Preskill, Protected gates for superconducting qubits, Phys. Rev. A 87, 052306 (2013).
  16. P. Groszkowski, A. D. Paolo, A. L. Grimsmo, A. Blais, D. I. Schuster, A. A. Houck, and J. Koch, Coherence properties of the 0-π qubit, New J. Phys. 20, 043053 (2018).
  17. A. Gyenis, P. S. Mundada, A. Di Paolo, T. M. Hazard, X. You, D. I. Schuster, J. Koch, A. Blais, and A. A. Houck, Experimental realization of a protected superconducting circuit derived from the 0–π qubit, PRX Quantum 2, 010339 (2021).
  18. R. S. Shaikhaidarov, K. H. Kim, J. W. Dunstan, I. V. Antonov, S. Linzen, M. Ziegler, D. S. Golubev, V. N. Antonov, E. V. Il’ichev, and O. V. Astafiev, Quantized current steps due to the a.c. coherent quantum phase-slip effect, Nature 608, 45 (2022).
  19. N. Crescini, S. Cailleaux, W. Guichard, C. Naud, O. Buisson, K. W. Murch, and N. Roch, Evidence of dual Shapiro steps in a Josephson junction array, Nat. Phys. 19, 851 (2023).
  20. F. Kaap, C. Kissling, V. Gaydamachenko, L. Grünhaupt, and S. Lotkhov, Demonstration of dual Shapiro steps in small Josephson junctions, Nat. Commun. 15, 8726 (2024).
  21. I. V. Pechenezhskiy, R. A. Mencia, L. B. Nguyen, Y.-H. Lin, and V. E. Manucharyan, The superconducting quasicharge qubit, Nature 585, 368 (2020).
  22. C. Jünger, T. Chistolini, L. B. Nguyen, H. Kim, L. Chen, T. Ersevim, W. Livingston, G. Koolstra, D. I. Santiago, and I. Siddiqi, Implementation of scalable suspended superinductors, Appl. Phys. Lett. 126, 044003 (2025).
  23. S. Frasca, I. Arabadzhiev, S. B. De Puechredon, F. Oppliger, V. Jouanny, R. Musio, M. Scigliuzzo, F. Minganti, P. Scarlino, and E. Charbon, NbN films with high kinetic inductance for high-quality compact superconducting resonators, Phys. Rev. Appl. 20, 044021 (2023).
  24. M. Peruzzo, A. Trioni, F. Hassani, M. Zemlicka, and J. M. Fink, Surpassing the resistance quantum with a geometric superinductor, Phys. Rev. Appl. 14, 044055 (2020).
  25. M. Medahinne, Y. P. Kandel, S. T. Magar, E. Champion, J. M. Nichol, and M. S. Blok, Magnetic-field-tolerant superconducting spiral resonators for circuit quantum electrodynamics, Phys. Rev. Appl. 23, 014070 (2025).
  26. M. Pita-Vidal, J. J. Wesdorp, L. J. Splitthoff, A. Bargerbos, Y. Liu, L. P. Kouwenhoven, and C. K. Andersen, Strong tunable coupling between two distant superconducting spin qubits, Nat. Phys. 20, 1158 (2024).
  27. T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygård, and C. M. Marcus, Semiconductor-nanowire-based superconducting qubit, Phys. Rev. Lett. 115, 127001 (2015).
  28. M. Valentini, F. Peñaranda, A. Hofmann, M. Brauns, R. Hauschild, P. Krogstrup, P. San-Jose, E. Prada, R. Aguado, and G. Katsaros, Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states, Science 373, 82 (2021).
  29. F. Luthi, T. Stavenga, O. W. Enzing, A. Bruno, C. Dickel, N. K. Langford, M. A. Rol, T. S. Jespersen, J. Nygård, P. Krogstrup, and L. DiCarlo, Evolution of nanowire transmon qubits and their coherence in a magnetic field, Phys. Rev. Lett. 120, 100502 (2018).
  30. D. Niepce, J. Burnett, and J. Bylander, High kinetic inductance NbN nanowire superinductors, Phys. Rev. Appl. 11, 044014 (2019).
  31. M. Yang, X. He, W. Gao, J. Chen, Y. Wu, X. Wang, G. Mu, W. Peng, and Z. Lin, Kinetic inductance compact resonator with NbTiN micronwires, AIP Adv. 14, 085027 (2024).
  32. A. Shearrow, G. Koolstra, S. J. Whiteley, N. Earnest, P. S. Barry, F. J. Heremans, D. D. Awschalom, E. Shirokoff, and D. I. Schuster, Atomic layer deposition of titanium nitride for quantum circuits, Appl. Phys. Lett. 113, 212601 (2018).
  33. K. R. Amin, C. Ladner, G. Jourdan, S. Hentz, N. Roch, and J. Renard, Loss mechanisms in tin high impedance superconducting microwave circuits, Appl. Phys. Lett. 120, 164001 (2022).
  34. M. R. Vissers, J. Gao, D. S. Wisbey, D. A. Hite, C. C. Tsuei, A. D. Corcoles, M. Steffen, and D. P. Pappas, Low loss superconducting titanium nitride coplanar waveguide resonators, Appl. Phys. Lett. 97, 232509 (2010).
  35. N. Samkharadze, A. Bruno, P. Scarlino, G. Zheng, D. P. DiVincenzo, L. DiCarlo, and L. M. K. Vandersypen, High-kinetic-inductance superconducting nanowire resonators for circuit QED in a magnetic field, Phys. Rev. Appl. 5, 044004 (2016).
  36. J. G. Kroll, F. Borsoi, K. L. Van Der Enden, W. Uilhoorn, D. De Jong, M. Quintero-Pérez, D. J. Van Woerkom, A. Bruno, S. R. Plissard, D. Car, E. P. A. M. Bakkers, M. C. Cassidy, and L. P. Kouwenhoven, Magnetic-field-resilient superconducting coplanar-waveguide resonators for hybrid circuit quantum electrodynamics experiments, Phys. Rev. Appl. 11, 064053 (2019).
  37. M. Müller, T. Luschmann, A. Faltermeier, S. Weichselbaumer, L. Koch, G. B. P. Huber, H. W. Schumacher, N. Ubbelohde, D. Reifert, T. Scheller, F. Deppe, A. Marx, S. Filipp, M. Althammer, R. Gross, and H. Huebl, Magnetic field robust high quality factor NbTiN superconducting microwave resonators, Mater. Quantum. Technol. 2, 015002 (2022).
  38. R. Gao, H. Ku, H. Deng, W. Yu, T. Xia, F. Wu, Z. Song, M. Wang, X. Miao, C. Zhang, Y. Lin, Y. Shi, H. Zhao, and C. Deng, Ultrahigh kinetic inductance superconducting materials from spinodal decomposition, Adv. Mater. 34, 2201268 (2022).
  39. H. Rotzinger, S. T. Skacel, M. Pfirrmann, J. N. Voss, J. Münzberg, S. Probst, P. Bushev, M. P. Weides, A. V. Ustinov, and J. E. Mooij, Aluminium-oxide wires for superconducting high kinetic inductance circuits, Supercond. Sci. Technol. 30, 025002 (2016).
  40. P. Kamenov, W.-S. Lu, K. Kalashnikov, T. DiNapoli, M. T. Bell, and M. E. Gershenson, Granular aluminum meandered superinductors for quantum circuits, Phys. Rev. Appl. 13, 054051 (2020).
  41. M. Janík, K. Roux, C. B. Espinosa, O. Sagi, A. Baghdadi, T. Adletzberger, S. Calcaterra, M. Botifoll, A. G. Manjón, J. Arbiol, D. Chrastina, G. Isella, I. M. Pop, and G. Katsaros, Strong charge-photon coupling in planar germanium enabled by granular aluminium superinductors, Nat. Commun. 16, 2103 (2025).
  42. V. Gupta, P. Winkel, N. Thakur, P. van Vlaanderen, Y. Wang, S. Ganjam, L. Frunzio, and R. J. Schoelkopf, Low loss lumped-element inductors made from granular aluminum, Phys. Rev. Appl. 23, 054067 (2025).
  43. M. Xu, R. Cheng, Y. Wu, G. Liu, and H. X. Tang, Magnetic field-resilient quantum-limited parametric amplifier, PRX Quantum 4, 010322 (2023).
  44. C. Joshi, W. Chen, H. G. LeDuc, P. K. Day, and M. Mirhosseini, Strong kinetic-inductance kerr nonlinearity with titanium nitride nanowires, Phys. Rev. Appl. 18, 064088 (2022).
  45. N. Maleeva, L. Grünhaupt, T. Klein, F. Levy-Bertrand, O. Dupre, M. Calvo, F. Valenti, P. Winkel, F. Friedrich, W. Wernsdorfer, A. V. Ustinov, H. Rotzinger, A. Monfardini, M. V. Fistul, and I. M. Pop, Circuit quantum electrodynamics of granular aluminum resonators, Nat. Commun. 9, 3889 (2018).
  46. P. Winkel, K. Borisov, L. Grünhaupt, D. Rieger, M. Spiecker, F. Valenti, A. V. Ustinov, W. Wernsdorfer, and I. M. Pop, Implementation of a transmon qubit using superconducting granular aluminum, Phys. Rev. X 10, 031032 (2020).
  47. C. Roy, S. Frasca, and P. Scarlino, Study of magnetic field resilient high impedance high-kinetic inductance superconducting resonators, arXiv:2503.13321.
  48. F. Levy-Bertrand, T. Klein, T. Grenet, O. Dupré, A. Benoît, A. Bideaud, O. Bourrion, M. Calvo, A. Catalano, A. Gomez, J. Goupy, L. Grünhaupt, U. V. Luepke, N. Maleeva, F. Valenti, I. M. Pop, and A. Monfardini, Electrodynamics of granular aluminum from superconductor to insulator: Observation of collective superconducting modes, Phys. Rev. B 99, 094506 (2019).
  49. M. Tinkham, Introduction to Superconductivity (Dover Publications, Mineola, 2004).
  50. A. J. Annunziata, D. F. Santavicca, L. Frunzio, G. Catelani, M. J. Rooks, A. Frydman, and D. E. Prober, Tunable superconducting nanoinductors, Nanotechnology 21, 445202 (2010).
  51. Z. K. Minev, I. M. Pop, and M. H. Devoret, Planar superconducting whispering gallery mode resonators, Appl. Phys. Lett. 103, 142604 (2013).
  52. U. S. Pracht, N. Bachar, L. Benfatto, G. Deutscher, E. Farber, M. Dressel, and M. Scheffler, Enhanced Cooper pairing versus suppressed phase coherence shaping the superconducting dome in coupled aluminum nanograins, Phys. Rev. B 93, 100503 (2016).
  53. F. Henriques, F. Valenti, T. Charpentier, M. Lagoin, C. Gouriou, M. Martínez, L. Cardani, M. Vignati, L. Grünhaupt, D. Gusenkova, J. Ferrero, S. T. Skacel, W. Wernsdorfer, A. V. Ustinov, G. Catelani, O. Sander, and I. M. Pop, Phonon traps reduce the quasiparticle density in superconducting circuits, Appl. Phys. Lett. 115, 212601 (2019).
  54. L. Grünhaupt, U. Von Lüpke, D. Gusenkova, S. T. Skacel, N. Maleeva, S. Schlör, A. Bilmes, H. Rotzinger, A. V. Ustinov, M. Weides, and I. M. Pop, An argon ion beam milling process for native AlOx layers enabling coherent superconducting contacts, Phys. Rev. Appl. 111, 072601 (2017).
  55. M. S. Bartlett, Smoothing periodograms from time-series with continuous spectra, Nature 161, 686 (1948).
  56. F. Valenti, F. Henriques, G. Catelani, N. Maleeva, L. Grünhaupt, U. Von Lüpke, S. T. Skacel, P. Winkel, A. Bilmes, A. V. Ustinov, J. Goupy, M. Calvo, A. Benoît, F. Levy-Bertrand, A. Monfardini, and I. M. Pop, Interplay between kinetic inductance, nonlinearity, and quasiparticle dynamics in granular aluminum microwave kinetic inductance detectors, Phys. Rev. Appl. 11, 054087 (2019).
  57. J. Burnett, A. Bengtsson, D. Niepce, and J. Bylander, Noise and loss of superconducting aluminium resonators at single photon energies, J. Phys. Conf. Ser. 969, 012131 (2018).
  58. S. Schlör, J. Lisenfeld, C. Müller, A. Bilmes, A. Schneider, D. P. Pappas, A. V. Ustinov, and M. Weides, Correlating decoherence in transmon qubits: Low frequency noise by single fluctuators, Phys. Rev. Lett. 123, 190502 (2019).
  59. M. Kristen, J. N. Voss, M. Wildermuth, H. Rotzinger, and A. V. Ustinov, Random telegraph fluctuations in granular microwave resonators, Appl. Phys. Lett. 122, 202602 (2023).
  60. D. Rieger, S. Günzler, M. Spiecker, A. Nambisan, W. Wernsdorfer, and I. M. Pop, Fano interference in microwave resonator measurements, Phys. Rev. Appl. 20, 014059 (2023).
  61. L. Grünhaupt, N. Maleeva, S. T. Skacel, M. Calvo, F. Levy-Bertrand, A. V. Ustinov, H. Rotzinger, A. Monfardini, G. Catelani, and I. M. Pop, Loss mechanisms and quasiparticle dynamics in superconducting microwave resonators made of thin-film granular aluminum, Phys. Rev. Lett. 121, 117001 (2018).
  62. S. Hunklinger, W. Arnold, S. Stein, R. Nava, and K. Dransfeld, Saturation of the ultrasonic absorption in vitreous silica at low temperatures, Phys. Lett. A 42, 253 (1972).
  63. B. Golding, J. E. Graebner, B. I. Halperin, and R. J. Schutz, Nonlinear phonon propagation in fused silica below 1 K, Phys. Rev. Lett. 30, 223 (1973).
  64. E. M. Levenson-Falk, F. Kos, R. Vijay, L. Glazman, and I. Siddiqi, Single-quasiparticle trapping in aluminum nanobridge Josephson junctions, Phys. Rev. Lett. 112, 047002 (2014).
  65. S. Gustavsson, F. Yan, G. Catelani, J. Bylander, A. Kamal, J. Birenbaum, D. Hover, D. Rosenberg, G. Samach, A. P. Sears, S. J. Weber, J. L. Yoder, J. Clarke, A. J. Kerman, F. Yoshihara, Y. Nakamura, T. P. Orlando, and W. D. Oliver, Suppressing relaxation in superconducting qubits by quasiparticle pumping, Science 354, 1573 (2016).
  66. H. Jin, G. Serpico, Y. Lee, T. Confalone, C. N. Saggau, F. Lo Sardo, G. Gu, B. H. Goodge, E. Lesne, D. Montemurro, K. Nielsch, N. Poccia, and U. Vool, Exploring van der Waals cuprate superconductors using a hybrid microwave circuit, Nano Lett. 25, 3191 (2025).
  67. G. Andersson, A. L. O. Bilobran, M. Scigliuzzo, M. M. de Lima, J. H. Cole, and P. Delsing, Acoustic spectral hole-burning in a two-level system ensemble, npj Quantum Inf. 7, 1 (2021).
  68. T. Capelle, E. Flurin, E. Ivanov, J. Palomo, M. Rosticher, S. Chua, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, Probing a two-level system bath via the frequency shift of an off-resonantly driven cavity, Phys. Rev. Appl. 13, 034022 (2020).
  69. N. Kirsh, E. Svetitsky, A. L. Burin, M. Schechter, and N. Katz, Revealing the nonlinear response of a tunneling two-level system ensemble using coupled modes, Phys. Rev. Mater. 1, 012601 (2017).
  70. M. Khorramshahi, zenodo, 2024, http://doi.org/10.5281/zenodo.16566910.
  71. F. R. Zypman, Mathematical expression for the capacitance of coplanar strips, J. Electrostat. 101, 103371 (2019).

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