- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Stacked Josephson junctions for quantum circuit applications

Alex Kreuzer1, Thilo Krumrey1, Hossam Tohamy1, Alexandru Ionita1, Hannes Rotzinger1,2,*, and Alexey V. Ustinov1,2

  • *Contact author: rotzinger@kit.edu
PDF

Phys. Rev. Applied 25, 064027 – Published 5 June, 2026

DOI: https://doi.org/10.1103/klgx-jff9

Abstract

Low-loss inductors are essential components in various superconducting circuits, such as qubits or digital electronics. In this study, we investigate highly compact inductors formed by vertically stacking Josephson junctions. Our implementation employs several layers of aluminum separated by tunnel barriers. Individual stacks are connected by suspended superconducting bridges, which are free of additional dielectric materials and, therefore, should not contribute significantly to losses. We present implementation details, fabrication results, and device characterization measurements.

View figure in article

Physics Subject Headings (PhySH)

See Also

Hyperinductance based on stacked Josephson junctions

P. Manset, J. Palomo, A. Schmitt, K. Gerashchenko, R. Rousseau, H. Patange, P. Abgrall, M. Houzet, E. Flurin, S. Deléglise, T. Jacqmin, and L. Balembois
Phys. Rev. Applied 25, 064028 (2026)

Article Text

References (52)

  1. A. Dacca, G. Gemme, R. Musenich, R. Parodi, S. Pittaluga, S. Rizzini, and V. Buscaglia, in 8th Workshop on RF Superconductivity (Istituto Nazionale di Fisica Nucleare, Rome, Italy, 1997), p. 1103.
  2. S. Mitra, G. C. Tewari, D. Mahalu, and D. Shahar, Negative magnetoresistance in amorphous indium oxide wires, Sci. Rep. 6, 37687 (2016).
  3. 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 (2017).
  4. D. Niepce, J. Burnett, and J. Bylander, High kinetic inductance NbN nanowire superinductors, Phys. Rev. Appl. 11, 044014 (2019).
  5. N. Kirsh, E. Svetitsky, S. Goldstein, G. Pardo, O. Hachmo, and N. Katz, Linear and nonlinear properties of a compact high-kinetic-inductance WSi multimode resonator, Phys. Rev. Appl. 16, 044017 (2021).
  6. 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).
  7. M. Kristen, J. N. Voss, M. Wildermuth, A. Bilmes, J. Lisenfeld, H. Rotzinger, and A. V. Ustinov, Giant two-level systems in a granular superconductor, Phys. Rev. Lett. 132, 217002 (2024).
  8. J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, Josephson persistent-current qubit, Science 285, 1036 (1999).
  9. 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).
  10. F. Yan, Y. Sung, P. Krantz, A. Kamal, D. K. Kim, J. L. Yoder, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Engineering framework for optimizing superconducting qubit designs, ArXiv:2006.04130.
  11. R. Kuzmin, N. Mehta, N. Grabon, and V. E. Manucharyan, Tuning the inductance of Josephson junction arrays without SQUIDs, Appl. Phys. Lett. 123, 182602 (2023).
  12. W. Zhang, K. Kalashnikov, W.-S. Lu, P. Kamenov, T. DiNapoli, and M. E. Gershenson, Microresonators fabricated from high-kinetic-inductance aluminum films, Phys. Rev. Appl. 11, 011003(R) (2019).
  13. J. Basset, D. Watfa, G. Aiello, M. Féchant, A. Morvan, J. Estève, J. Gabelli, M. Aprili, R. Weil, A. Kasumov, H. Bouchiat, and R. Deblock, High kinetic inductance microwave resonators made by He-beam assisted deposition of tungsten nanowires, Appl. Phys. Lett. 114, 102601 (2019).
  14. S. Frasca, I. N. Arabadzhiev, S. Y. 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).
  15. 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).
  16. T. C. White et al., Traveling wave parametric amplifier with Josephson junctions using minimal resonator phase matching, Appl. Phys. Lett. 106, 242601 (2015).
  17. C. Macklin, K. O’Brien, D. Hover, M. E. Schwartz, V. Bolkhovsky, X. Zhang, W. D. Oliver, and I. Siddiqi, A near–quantum-limited Josephson traveling-wave parametric amplifier, Science 350, 307 (2015).
  18. F. Faramarzi, R. Stephenson, S. Sypkens, B. H. Eom, H. LeDuc, and P. Day, A 4–8 GHz kinetic inductance traveling-wave parametric amplifier using four-wave mixing with near quantum-limited noise performance, APL Quantum 1, 036107 (2024).
  19. A. Giachero, M. Vissers, J. Wheeler, L. Howe, J. Gao, J. Austermann, J. Hubmayr, A. Nucciotti, and J. Ullom, Kinetic inductance traveling wave amplifier designs for practical microwave readout applications, J. Low Temp. Phys. 215, 152 (2024).
  20. V. Kaplunenko and G. M. Fischer, Josephson junction arrays as a variable inductor in RF circuits and tunable filters, Supercond. Sci. Technol. 17, S145 (2004).
  21. C. Altimiras, O. Parlavecchio, P. Joyez, D. Vion, P. Roche, D. Esteve, and F. Portier, Tunable microwave impedance matching to a high impedance source using a Josephson metamaterial, Appl. Phys. Lett. 103, 212601 (2013).
  22. S. K. Tolpygo, Superconductor digital electronics: Scalability and energy efficiency issues (Review article), Low Temp. Phys. 42, 361 (2016).
  23. S. K. Tolpygo, V. Bolkhovsky, D. E. Oates, R. Rastogi, S. Zarr, A. L. Day, T. J. Weir, A. Wynn, and L. M. Johnson, Superconductor electronics fabrication process with MoNx kinetic inductors and self-shunted Josephson junctions, IEEE Trans. Appl. Supercond. 28, 1100212 (2018).
  24. A. E. Fox, G. Butler, M. Thompson, P. D. Dresselhaus, and S. P. Benz, Induced current effects in Josephson voltage standard circuits, IEEE Trans. Appl. Supercond. 29, 1101808 (2019).
  25. M. A. Castellanos-Beltran, D. I. Olaya, A. J. Sirois, P. D. Dresselhaus, S. P. Benz, and P. F. Hopkins, Stacked Josephson junctions as inductors for single flux quantum circuits, IEEE Trans. Appl. Supercond. 29, 1300705 (2019).
  26. S. K. Tolpygo, J. L. Mallek, V. Bolkhovsky, R. Rastogi, E. B. Golden, T. J. Weir, L. M. Johnson, and M. A. Gouker, Progress toward superconductor electronics fabrication process with planarized NbN and NbN/Nb layers, IEEE Trans. Appl. Supercond. 33, 1101512 (2023).
  27. K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon and Breach Science Publishers, Amsterdam, the Netherlands, 1986).
  28. I. V. Pechenezhskiy, R. A. Mencia, L. B. Nguyen, Y.-H. Lin, and V. E. Manucharyan, The superconducting quasicharge qubit, Nature 585, 368 (2020).
  29. M. T. Bell, I. A. Sadovskyy, L. B. Ioffe, A. Y. Kitaev, and M. E. Gershenson, Quantum superinductor with tunable nonlinearity, Phys. Rev. Lett. 109, 137003 (2012).
  30. A. V. Ustinov, H. Kohlstedt, M. Cirillo, N. F. Pedersen, G. Hallmanns, and C. Heiden, Coupled fluxon modes in stacked Nb/AlOx/Nb long Josephson junctions, Phys. Rev. B 48, 10614 (1993).
  31. S. Sakai, A. V. Ustinov, H. Kohlstedt, A. Petraglia, and N. F. Pedersen, Theory and experiment on electromagnetic-wave-propagation velocities in stacked superconducting tunnel structures, Phys. Rev. B 50, 12905 (1994).
  32. N. F. Pedersen and A. V. Ustinov, Fluxons in Josephson transmission lines: New developments, Supercond. Sci. Technol. 8, 389 (1995).
  33. A. V. Ustinov and H. Kohlstedt, Interlayer fluxon interaction in Josephson stacks, Phys. Rev. B 54, 6111 (1996).
  34. S. V. Shitov, A. V. Ustinov, N. Iosad, and H. Kohlstedt, On-chip radiation detection from stacked Josephson flux-flow oscillators, J. Appl. Phys. 80, 7134 (1996).
  35. R. M. Bradley and S. Doniach, Quantum fluctuations in chains of Josephson junctions, Phys. Rev. B 30, 1138 (1984).
  36. L. I. Glazman and A. I. Larkin, New quantum phase in a one-dimensional Josephson array, Phys. Rev. Lett. 79, 3736 (1997).
  37. K. A. Matveev, M. Gisselfält, L. I. Glazman, M. Jonson, and R. I. Shekhter, Parity-induced suppression of the Coulomb blockade of Josephson tunneling, Phys. Rev. Lett. 70, 2940 (1993).
  38. D. B. Haviland, K. Andersson, and P. Ågren, Superconducting and insulating behavior in one-dimensional Josephson junction arrays, J. Low Temp. Phys. 118, 733 (2000).
  39. 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).
  40. 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).
  41. 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).
  42. I. M. Pop, I. Protopopov, F. Lecocq, Z. Peng, B. Pannetier, O. Buisson, and W. Guichard, Measurement of the effect of quantum phase slips in a Josephson junction chain, Nat. Phys. 6, 589 (2010).
  43. Ansys, Inc., Ansys Maxwell: Low Frequency EM Field Simulation, https://www.ansys.com/products/electronics/ansys-maxwell (2023), accessed: 2025-11-25.
  44. S. V. Lotkhov, E. M. Tolkacheva, D. V. Balashov, M. I. Khabipov, F.-I. Buchholz, and A. B. Zorin, Low hysteretic behavior of Al/AlOxAl Josephson junctions, Appl. Phys. Lett. 89, 132115 (2006).
  45. S. Ó Peatáin, T. Dixon, P. J. Meeson, J. M. Williams, S. Kafanov, and Y. A. Pashkin, Simulating the effects of fabrication tolerance on the performance of Josephson travelling wave parametric amplifiers, Supercond. Sci. Technol. 36, 045017 (2023).
  46. M. V. Fistul, V. M. Vinokur, and T. I. Baturina, Macroscopic Coulomb blockade in large Josephson junction arrays, ArXiv:0806.4311.
  47. S. Feldman and A. Rogachev, Quantum phase transition in small-size 1D and 2D Josephson junction arrays: Analysis of the experiments within the interacting plasmons picture, ArXiv:2411.06492.
  48. T. Weißl, B. Küng, E. Dumur, A. K. Feofanov, I. Matei, C. Naud, O. Buisson, F. W. J. Hekking, and W. Guichard, Kerr coefficients of plasma resonances in Josephson junction chains, Phys. Rev. B 92, 104508 (2015).
  49. V. Ambegaokar and A. Baratoff, Tunneling between superconductors, Phys. Rev. Lett. 10, 486 (1963).
  50. D. M. Basko and F. W. J. Hekking, Disordered Josephson junction chains: Anderson localization of normal modes and impedance fluctuations, Phys. Rev. B 88, 094507 (2013).
  51. D. V. Nguyen and D. M. Basko, Inhomogeneous Josephson junction chains: A superconducting meta-material for superinductance optimization, Eur. Phys. J. Spec. Top. 226, 1499 (2017).
  52. A. Kleinsasser, R. Miller, and W. Mallison, Dependence of critical current density on oxygen exposure in Nb-AlOx-Nb tunnel junctions, IEEE Trans. Appl. Supercond. 5, 26 (1995).

Outline

Information

Phys. Rev. Applied 25, 064027– Published 5 June, 2026
  • Received 3 June 2025
  • Revised 30 September 2025
  • Accepted 14 April 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation