Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Granular aluminium nanojunction fluxonium qubit

Abstract

Mesoscopic Josephson junctions, consisting of overlapping superconducting electrodes separated by a nanometre-thin oxide layer, provide a precious source of nonlinearity for superconducting quantum circuits. Here we show that in a fluxonium qubit, the role of the Josephson junction can also be played by a lithographically defined, self-structured granular aluminium nanojunction: a superconductor–insulator–superconductor Josephson junction obtained in a single-layer, zero-angle evaporation. The measured spectrum of the resulting qubit, which we nickname gralmonium, is indistinguishable from that of a standard fluxonium. Remarkably, the lack of a mesoscopic parallel plate capacitor gives rise to an intrinsically large granular aluminium nanojunction charging energy in the range of tens of gigahertz, comparable to its Josephson energy. We measure coherence times in the microsecond range and we observe spontaneous jumps of the value of the Josephson energy on timescales from milliseconds to days, which offers a powerful diagnostics tool for microscopic defects in superconducting materials.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The gralmonium, a single-layer grAl fluxonium circuit.
Fig. 2: Gralmonium spectroscopy versus external flux.
Fig. 3: Time domain characterization of the gralmonium at half-flux bias.

Data availability

All relevant data are available from the corresponding authors upon reasonable request.

References

  1. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).

    Article  CAS  Google Scholar 

  2. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article  Google Scholar 

  3. Manucharyan, V. E., Koch, J., Glazman, L. I. & Devoret, M. H. Fluxonium: single Cooper pair circuit free of charge offsets. Science 326, 113–116 (2009).

    Article  CAS  Google Scholar 

  4. Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y.-x. & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718–719, 1–102 (2017).

    Article  Google Scholar 

  5. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021).

    Article  CAS  Google Scholar 

  6. Kandala, A. et al. Error mitigation extends the computational reach of a noisy quantum processor. Nature 567, 491–495 (2019).

    Article  CAS  Google Scholar 

  7. Gold, A. et al. Entanglement across separate silicon dies in a modular superconducting qubit device. npj Quantum Inf. 7, 142 (2021).

    Article  Google Scholar 

  8. Bao, F. et al. Fluxonium: an alternative qubit platform for high-fidelity operations. Phys. Rev. Lett. 129, 010502 (2022).

    Article  CAS  Google Scholar 

  9. McEwen, M. et al. Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits. Nat. Phys. 18, 107–111 (2022).

    Article  CAS  Google Scholar 

  10. Josephson, B. Possible new effects in superconductive tunnelling. Phys. Lett. 1, 251–253 (1962).

    Article  Google Scholar 

  11. Kreikebaum, J. M., O’Brien, K. P., Morvan, A. & Siddiqi, I. Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits. Supercond. Sci. Technol. 33, 06LT02 (2020).

    Article  Google Scholar 

  12. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011).

    Article  Google Scholar 

  13. Somoroff, A. et al. Millisecond coherence in a superconducting qubit. Preprint at https://arxiv.org/abs/2103.08578 (2021).

  14. Siddiqi, I. Engineering high-coherence superconducting qubits. Nat. Rev. Mater. 6, 875–891 (2021).

    Article  Google Scholar 

  15. Krause, J. et al. Magnetic field resilience of three-dimensional transmons with thin-film Al/AlOx/Al Josephson junctions approaching 1 T. Phys. Rev. Appl. 17, 034032 (2022).

    Article  CAS  Google Scholar 

  16. Clerk, A. A., Lehnert, K. W., Bertet, P., Petta, J. R. & Nakamura, Y. Hybrid quantum systems with circuit quantum electrodynamics. Nat. Phys. 16, 257–267 (2020).

    Article  CAS  Google Scholar 

  17. Kurizki, G. et al. Quantum technologies with hybrid systems. Proc. Natl Acad. Sci. USA 112, 3866–3873 (2015).

    Article  CAS  Google Scholar 

  18. Groszkowski, P. et al. Coherence properties of the 0-π qubit. New J. Phys. 20, 043053 (2018).

    Article  Google Scholar 

  19. Peruzzo, M. et al. Geometric superinductance qubits: controlling phase delocalization across a single Josephson junction. PRX Quantum 2, 040341 (2021).

    Article  Google Scholar 

  20. Janvier, C. et al. Coherent manipulation of Andreev states in superconducting atomic contacts. Science 349, 1199–1202 (2015).

    Article  CAS  Google Scholar 

  21. Hays, M. et al. Coherent manipulation of an Andreev spin qubit. Science 373, 430–433 (2021).

    Article  CAS  Google Scholar 

  22. Pita-Vidal, M. et al. Gate-tunable field-compatible fluxonium. Phys. Rev. Appl. 14, 064038 (2020).

    Article  CAS  Google Scholar 

  23. Tinkham, M. in Introduction to Superconductivity Ch. 6.1 (Dover Publications, 2004).

  24. Golubov, A. A., Kupriyanov, M. Y. & Il’ichev, E. The current-phase relation in Josephson junctions. Rev. Mod. Phys. 76, 411–469 (2004).

    Article  CAS  Google Scholar 

  25. Lam, S. K. H. Noise properties of SQUIDs made from nanobridges. Supercond. Sci. Technol. 19, 963–967 (2006).

    Article  CAS  Google Scholar 

  26. Astafiev, O. V. et al. Coherent quantum phase slip. Nature 484, 355–358 (2012).

    Article  CAS  Google Scholar 

  27. Peltonen, J. T. et al. Coherent dynamics and decoherence in a superconducting weak link. Phys. Rev. B 94, 180508 (2016).

    Article  Google Scholar 

  28. Grünhaupt, L. et al. Granular aluminium as a superconducting material for high-impedance quantum circuits. Nat. Mater. 18, 816–819 (2019).

    Article  Google Scholar 

  29. Zhang, H. et al. Universal fast-flux control of a coherent, low-frequency qubit. Phys. Rev. X 11, 011010 (2021).

    CAS  Google Scholar 

  30. Deutscher, G., Fenichel, H., Gershenson, M., Grünbaum, E. & Ovadyahu, Z. Transition to zero dimensionality in granular aluminum superconducting films. J. Low Temp. Phys. 10, 231–243 (1973).

    Article  CAS  Google Scholar 

  31. Glezer Moshe, A., Farber, E. & Deutscher, G. Granular superconductors for high kinetic inductance and low loss quantum devices. Appl. Phys. Lett. 117, 062601 (2020).

    Article  CAS  Google Scholar 

  32. Borisov, K. et al. Superconducting granular aluminum resonators resilient to magnetic fields up to 1 tesla. Appl. Phys. Lett. 117, 120502 (2020).

    Article  CAS  Google Scholar 

  33. Kou, A. et al. Simultaneous monitoring of fluxonium qubits in a waveguide. Phys. Rev. Appl. 9, 064022 (2018).

    Article  CAS  Google Scholar 

  34. Cohen, R. W. & Abeles, B. Superconductivity in granular aluminum films. Phys. Rev. 168, 444–450 (1968).

    Article  CAS  Google Scholar 

  35. Voss, J. N. et al. Eliminating quantum phase slips in superconducting nanowires. ACS Nano 15, 4108–4114 (2021).

    Article  CAS  Google Scholar 

  36. Maleeva, N. et al. Circuit quantum electrodynamics of granular aluminum resonators. Nat. Commun. 9, 3889 (2018).

    Article  CAS  Google Scholar 

  37. Levy-Bertrand, F. et al. Electrodynamics of granular aluminum from superconductor to insulator: observation of collective superconducting modes. Phys. Rev. B 99, 094506 (2019).

    Article  CAS  Google Scholar 

  38. Winkel, P. et al. Nondegenerate parametric amplifiers based on dispersion-engineered Josephson-junction arrays. Phys. Rev. Appl. 13, 024015 (2020).

    Article  CAS  Google Scholar 

  39. Smith, W. C. et al. Quantization of inductively shunted superconducting circuits. Phys. Rev. B 94, 144507 (2016).

    Article  Google Scholar 

  40. Friedrich, F. et al. Onset of phase diffusion in high kinetic inductance granular aluminum micro-SQUIDs. Supercond. Sci. Technol. 32, 125008 (2019).

    Article  CAS  Google Scholar 

  41. Winkel, P. et al. Implementation of a transmon qubit using superconducting granular aluminum. Phys. Rev. X 10, 031032 (2020).

    CAS  Google Scholar 

  42. Gusenkova, D. et al. Quantum nondemolition dispersive readout of a superconducting artificial atom using large photon numbers. Phys. Rev. Appl. 15, 064030 (2021).

    Article  CAS  Google Scholar 

  43. Rastelli, G., Pop, I. M. & Hekking, F. W. J. Quantum phase slips in Josephson junction rings. Phys. Rev. B 87, 174513 (2013).

    Article  Google Scholar 

  44. Eckern, U., Schön, G. & Ambegaokar, V. Quantum dynamics of a superconducting tunnel junction. Phys. Rev. B 30, 6419–6431 (1984).

    Article  Google Scholar 

  45. Pop, I. M. et al. Experimental demonstration of Aharonov-Casher interference in a Josephson junction circuit. Phys. Rev. B 85, 094503 (2012).

    Article  Google Scholar 

  46. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Inf. 5, 105 (2019).

    Article  Google Scholar 

  47. Hertzberg, J. B. et al. Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors. npjQuantum Inf. 7, 129 (2021).

    Google Scholar 

  48. Frattini, N. E. et al. 3-wave mixing Josephson dipole element. Appl. Phys. Lett. 110, 222603 (2017).

    Article  Google Scholar 

  49. Beloborodov, I. S., Lopatin, A. V., Vinokur, V. M. & Efetov, K. B. Granular electronic systems. Rev. Mod. Phys. 79, 469–518 (2007).

    Article  CAS  Google Scholar 

  50. Sacépé, B., Feigel’man, M. & Klapwijk, T. M. Quantum breakdown of superconductivity in low-dimensional materials. Nat. Phys. 16, 734–746 (2020).

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to U. Vool for fruitful discussions, and we acknowledge technical support from S. Diewald, A. Eberhardt, M. K. Gamer, A. Lukashenko and L. Radtke. Funding is provided by the Alexander von Humboldt Foundation in the framework of a Sofja Kovalevskaja award endowed by the German Federal Ministry of Education and Research and by the European Union’s Horizon 2020 programme under grant no. 899561 (AVaQus). P.P. and I.M.P. acknowledge support from the German Ministry of Education and Research within the QUANTERA project SiUCs (FKZ, 13N15209). D.R., S.G., P.W. and W.W. acknowledge support from the European Research Council advanced grant MoQuOS (no. 741276). Facility use was supported by the Karlsruhe Nano Micro Facility and KIT Nanostructure Service Laboratory. We acknowledge qKit for providing a convenient measurement software framework.

Author information

Authors and Affiliations

Authors

Contributions

D.R., S.G., M.S. and I.M.P. conceived and designed the experiment. D.R. and S.G. performed the microwave simulation. P.P., L.H., J.K.H. and A.B. contributed to the device fabrication. D.R., S.G., M.S. and P.W. participated in the measurements. D.R. and S.G. analysed the data. D.R. and S.G. led the paper writing, and M.S., P.P., P.W., J.K.H., W.W. and I.M.P. contributed to the text. W.W. and I.M.P. supervised the project.

Corresponding authors

Correspondence to D. Rieger or I. M. Pop.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Ivan Pechenezhskiy and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–13 and Discussion.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rieger, D., Günzler, S., Spiecker, M. et al. Granular aluminium nanojunction fluxonium qubit. Nat. Mater. 22, 194–199 (2023). https://doi.org/10.1038/s41563-022-01417-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-022-01417-9

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing