The demonstration of coherent quantum phase slips (CQPS) in disordered superconductors has opened up a new route towards exploring the fundamental charge–phase duality in superconductors, with the promise of devices with new functionalities and a robust quantum current standard based on CQPS. Here we demonstrate a device that integrates several CQPS junctions: the charge quantum interference device. The charge quantum interference device becomes the dual of the well-known superconducting quantum interference device, and is a manifestation of the Aharonov–Casher effect in a continuous superconducting system devoid of dielectric barriers.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Additional information

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


  1. 1.

    Arutyunov, K. Y., Golubev, D. S. & Zaikin, A. D. Superconductivity in one dimension. Phys. Rep. 464, 1–70 (2008).

  2. 2.

    McCumber, D. E. & Halperin, B. I. Time scale of intrinsic resistive fluctuations in thin superconducting wires. Phys. Rev. B 1, 1054–1070 (1970).

  3. 3.

    Martinis, J. M., Devoret, M. H. & Clarke, J. Experimental tests for the quantum behavior of a macroscopic degree of freedom: the phase difference across a Josephson junction. Phys. Rev. B 35, 4682–4698 (1987).

  4. 4.

    Mooij, J. E. & Nazarov, Y. V. Superconducting nanowires as quantum phase-slip junctions. Nat. Phys. 2, 169–172 (2006).

  5. 5.

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

  6. 6.

    Mooij, J. E. & Harmans, C. J. P. M. Phase-slip flux qubits. New. J. Phys. 7, 219 (2005).

  7. 7.

    Hriscu, A. M. & Nazarov, Y. V. Coulomb blockade due to quantum phase slips illustrated with devices. Phys. Rev. B 83, 174511 (2011).

  8. 8.

    Jaklevic, R. C., Lambe, J., Silver, A. H. & Mercereau, J. E. Quantum interference effects in Josephson tunneling. Phys. Rev. Lett. 12, 159–160 (1964).

  9. 9.

    Shapiro, S. Josephson currents in superconducting tunneling: The effect of microwaves and other observations. Phys. Rev. Lett. 11, 80–82 (1963).

  10. 10.

    Kohlmann, J., Behr, R. & Funck, T. Josephson voltage standards. Meas. Sci. Tech. 14, 1216–1228 (2003).

  11. 11.

    Gallop, J. C. SQUIDs, the Josephson Effects and Superconducting Electronics (IOP Publishing Ltd., Bristol, 1990).

  12. 12.

    Ergül, A. et al. Localising quantum phase slips in one-dimensional Josephson junction chains. New. J. Phys. 15, 095014 (2013).

  13. 13.

    Webster, C. H. et al. NbSi nanowire quantum phase slip circuits: dc supercurrent blockade, microwave measurements, and thermal analysis. Phys. Rev. B 87, 144510 (2013).

  14. 14.

    Peltonen, J. T. et al. Coherent flux tunneling through NbN nanowires. Phys. Rev. B 88, 220506 (2013).

  15. 15.

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

  16. 16.

    Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).

  17. 17.

    Aharonov, Y. & Casher, A. Topological quantum effects for neutral particles. Phys. Rev. Lett. 53, 319–321 (1984).

  18. 18.

    Elion, W. J., Wachters, J. J., Sohn, L. L. & Mooij, J. E. Observation of the Aharonov–Casher effect in vortices in Josephson-junction arrays. Phys. Rev. Lett. 71, 2311–2314 (1993).

  19. 19.

    Cimmino, A. et al. Observation of the topological Aharonov–Casher phase shift by neutron interferometry. Phys. Rev. Lett. 63, 380–383 (1989).

  20. 20.

    Sangster, K., Hinds, E. A., Barnett, S. M. & Riis, E. Measurement of the Aharonov–Casher phase in an atomic system. Phys. Rev. Lett. 71, 3641–3644 (1993).

  21. 21.

    König, M. et al. Direct observation of the Aharonov–Casher phase. Phys. Rev. Lett. 96, 076804 (2006).

  22. 22.

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

  23. 23.

    Bell, M. T., Zhang, W., Ioffe, L. B. & Gershenson, M. E. Spectroscopic evidence of the Aharonov–Casher effect in a Cooper pair box. Phys. Rev. Lett. 116, 107002 (2016).

  24. 24.

    Born, D. et al. Reading out the state inductively and microwave spectroscopy of an interferometer-type charge qubit. Phys. Rev. B 70, 180501 (2004).

  25. 25.

    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).

  26. 26.

    Manucharyan, V. E. et al. Evidence for coherent quantum phase slips across a Josephson junction array. Phys. Rev. B 85, 024521 (2012).

  27. 27.

    Masluk, N. A., Pop, I. M., Kamal, A., Minev, Z. K. & Devoret, M. H. Microwave characterisation of Josephson junction arrays: Implementing a low loss superinductance. Phys. Rev. Lett. 109, 137002 (2012).

  28. 28.

    Kerman, A. J. Fluxcharge duality and topological quantum phase fluctuations in quasi-one-dimensional superconductors. New. J. Phys. 15, 105017 (2013).

  29. 29.

    Guichard, W. & Hekking, F. W. J. Phase-charge duality in Josephson junction circuits: Role of inertia and effect of microwave irradiation. Phys. Rev. B 81, 064508 (2010).

  30. 30.

    Friedman, J. R. & Averin, D. V. Aharonov–Casher-effect suppression of macroscopic tunneling of magnetic flux. Phys. Rev. Lett. 88, 050403 (2002).

  31. 31.

    Weißl, T. et al. Bloch band dynamics of a Josephson junction in an inductive environment. Phys. Rev. B 91, 014507 (2015).

  32. 32.

    Cedergren, K. et al. Insulating Josephson junction chains as pinned Luttinger liquids. Phys. Rev. Lett. 119, 167701 (2017).

  33. 33.

    Linzen, S. et al. Structural and electrical properties of ultrathin niobium nitride films grown by atomic layer deposition. Supercond. Sci. Technol. 30, 035010 (2017).

  34. 34.

    Ziegler, M. et al. Superconducting niobium nitride thin films deposited by metal organic plasma-enhanced atomic layer deposition. Supercond. Sci. Technol. 26, 025008 (2013).

  35. 35.

    Ziegler, M. et al. Effects of plasma parameter on morphological and electrical properties of superconducting NbN fabricated by MO-PEALD. IEEE Trans. Appl. Supercond. 27, 7501307 (2017).

  36. 36.

    Hongisto, T. T. & Zorin, A. B. Single-charge transistor based on the charge–phase duality of a superconducting nanowire. Phys. Rev. Lett. 108, 097001 (2012).

  37. 37.

    Lehtinen, J. S., Zakharov, K. & Arutyunov, K. Y. Coulomb blockade and Bloch oscillations in superconducting Ti nanowires. Phys. Rev. Lett. 109, 187001 (2012).

  38. 38.

    Kafanov, S. & Chtchelkatchev, N. M. Single flux transistor: The controllable interplay of coherent quantum phase slip and flux quantization. J. Appl. Phys. 114, 073907 (2013).

  39. 39.

    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).

  40. 40.

    Hu, Z., Tie-Fu, L., Jian-She, L. & Wai, C. Charge-related SQUID and tunable phase-slip flux qubit. Chinese Phys. Lett. 31, 030303 (2014).

  41. 41.

    Matveev, K. A., Larkin, A. I. & Glazman, L. I. Persistent current in superconducting nanorings. Phys. Rev. Lett. 89, 096802 (2002).

  42. 42.

    Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011).

  43. 43.

    Eiles, T. M., Martinis, J. M. & Devoret, M. H. Even–odd asymmetry of a superconductor revealed by the Coulomb blockade of Andreev reflection. Phys. Rev. Lett. 70, 1862–1865 (1993).

  44. 44.

    Hekking, F. W. J., Glazman, L. I., Matveev, K. A. & Shekhter, R. I. Coulomb blockade of two-electron tunneling. Phys. Rev. Lett. 70, 4138–4141 (1993).

  45. 45.

    Sun, L. et al. Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit. Phys. Rev. Lett. 108, 230509 (2012).

  46. 46.

    Vanjevic, M. & Nazarov, Y. V. Quantum phase slips in superconducting wires with weak homogeneities. Phys. Rev. Lett. 108, 187002 (2012).

  47. 47.

    Semenov, A. D., Goltsman, G. N. & Korneev, A. A. Quantum detection by current carrying superconducting film. Phys. C 351, 349–356 (2001).

  48. 48.

    Vora, H., Kautz, R. L., Nam, S. W. & Aumentado, J. Modeling Bloch oscillations in nanoscale Josephson junctions. Phys. Rev. B 96, 054505 (2017).

Download references


This work was supported by the UK government’s Department for Business, Energy and Industrial Strategy. We thank Y. Nazarov and A. Semenov for fruitful discussions. S.T.S. thanks S. Diewald and L. Radtke for their technical support during fabrication and acknowledges support from the Heinrich Böll Foundation and the KHYS. This work was partially supported by the Increase Competitiveness Program of the NUST MISiS (grants no. K2-2015-002 and 2-2016-051).

Author information


  1. National Physical Laboratory, Teddington, UK

    • S. E. de Graaf
    • , T. Hönigl-Decrinis
    • , A. Ya. Tzalenchuk
    •  & O. V. Astafiev
  2. Physikalisches Institut, Karlsruhe Institute of Technology, Karlsruhe, Germany

    • S. T. Skacel
    • , H. Rotzinger
    •  & A. V. Ustinov
  3. Department of Physics, Royal Holloway University of London, Egham, UK

    • T. Hönigl-Decrinis
    • , R. Shaikhaidarov
    • , V. Antonov
    • , A. Ya. Tzalenchuk
    •  & O. V. Astafiev
  4. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    • R. Shaikhaidarov
    •  & O. V. Astafiev
  5. Leibniz Institute of Photonic Technology, Jena, Germany

    • S. Linzen
    • , M. Ziegler
    • , U. Hübner
    • , H.-G. Meyer
    •  & E. Il’ichev
  6. Skolkovo Institute of Science and Technology, Moscow, Russia

    • V. Antonov
  7. Russian Quantum Center, National University of Science and Technology MISIS, Moscow, Russia

    • E. Il’ichev
    • , A. V. Ustinov
    •  & O. V. Astafiev


  1. Search for S. E. de Graaf in:

  2. Search for S. T. Skacel in:

  3. Search for T. Hönigl-Decrinis in:

  4. Search for R. Shaikhaidarov in:

  5. Search for H. Rotzinger in:

  6. Search for S. Linzen in:

  7. Search for M. Ziegler in:

  8. Search for U. Hübner in:

  9. Search for H.-G. Meyer in:

  10. Search for V. Antonov in:

  11. Search for E. Il’ichev in:

  12. Search for A. V. Ustinov in:

  13. Search for A. Ya. Tzalenchuk in:

  14. Search for O. V. Astafiev in:


O.V.A., S.E.d.G. and A.Y.T. conceived the experiment. S.E.d.G. designed the samples, performed the measurements with assistance from S.T.S., T.H.-D., R.S., V.A. and O.V.A., and analysed the data. S.L., M.Z., U.H., H.G.M. and E.I. developed the thin-film technology. S.T.S. fabricated the samples with assistance from H.R. and R.S. S.E.d.G. wrote the manuscript with input from O.V.A., S.T.S. and all other authors. All authors discussed the results.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to S. E. de Graaf.

Supplementary information

About this article

Publication history




Issue Date



Further reading