Skip to main content

Thank you for visiting 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.

  • Letter
  • Published:

Quantum dynamics of a single vortex


Vortices occur naturally in a wide range of gases and fluids, from macroscopic to microscopic scales. In Bose–Einstein condensates of dilute atomic gases1, superfluid helium2 and superconductors, the existence of vortices is a consequence of the quantum nature of the system. Quantized vortices of supercurrent3 are generated by magnetic flux penetrating the material, and play a key role in determining the material properties4 and the performance of superconductor-based devices5,6. At high temperatures the dynamics of such vortices are essentially classical, while at low temperatures previous experiments have suggested collective quantum dynamics7,8. However, the question of whether vortex tunnelling occurs at low temperatures has been addressed only for large collections of vortices. Here we study the quantum dynamics of an individual vortex in a superconducting Josephson junction. By measuring the statistics of the vortex escape from a controllable pinning potential, we demonstrate the existence of quantized levels of the vortex energy within the trapping potential well and quantum tunnelling of the vortex through the pinning barrier.

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

Access options

Buy this article

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

Figure 1: Sample, vortex potential and switching current measurement.
Figure 2: Thermal activation and quantum tunnelling.
Figure 3: Vortex energy levels.

Similar content being viewed by others


  1. Abo-Shaeer, J. R., Raman, C., Vogels, J. M. & Ketterle, W. Observation of vortex lattices in Bose-Einstein condensates. Science 292, 476–479 (2001)

    Article  ADS  CAS  Google Scholar 

  2. Blaauwgeers, R. et al. Double-quantum vortex in superfluid 3He-A. Nature 404, 471–473 (2000)

    Article  ADS  CAS  Google Scholar 

  3. Huebener, R. P. Magnetic Flux Structures in Superconductors (Springer, Berlin, 2001)

    Book  Google Scholar 

  4. Bugoslavsky, Y., Perkins, G. K., Qi, X., Cohen, L. F. & Caplin, A. D. Vortex dynamics in superconducting MgB2 and prospects for applications. Nature 410, 563–565 (2001)

    Article  ADS  CAS  Google Scholar 

  5. Nori, F. & Savel'ev, S. Experimentally realizable devices for controlling the motion of magnetic flux quanta in anisotropic superconductors. Nature Mater. 1, 179–184 (2002)

    Article  ADS  Google Scholar 

  6. Lee, C.-S., Janko, B., Derenyi, I. & Barabesi, A.-L. Reducing the vortex density in superconductors using the ratchet effect. Nature 400, 337–340 (1999)

    Article  ADS  CAS  Google Scholar 

  7. Fazio, R. & van der Zant, H. J. S. Quantum phase transitions and vortex dynamics in superconducting networks. Phys. Rep. 355, 235–334 (2001)

    Article  ADS  CAS  Google Scholar 

  8. Blatter, G., Feigel'man, M. V., Geshkenbein, A. I. & Vinokur, V. M. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125–1388 (1994)

    Article  ADS  CAS  Google Scholar 

  9. Tinkham, M. Introduction to Superconductivity (McGraw-Hill International Editions, New York, 1996)

    Google Scholar 

  10. Clarke, J., Cleland, A. N., Devoret, M. H., Esteve, D. & Martinis, J. M. Quantum mechanics of a macroscopic variable: The phase difference of a Josephson junction. Science 239, 992–997 (1988)

    Article  ADS  CAS  Google Scholar 

  11. Devoret, M. H. et al. in Quantum Tunneling in Condensed Media, (eds Kagan, Yu. & Leggett, A. J.) (North-Holland, Amsterdam, 1992)

    Google Scholar 

  12. Bennett, C. H. & DiVincenzo, D. P. Quantum information and computation. Nature 404, 247–255 (2000)

    Article  ADS  CAS  Google Scholar 

  13. 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  ADS  CAS  Google Scholar 

  14. Friedman, J. R., Patel, V., Chen, W., Tolpygo, S. K. & Lukens, J. E. Quantum superposition of distinct macroscopic states. Nature 406, 43–46 (2000)

    Article  ADS  CAS  Google Scholar 

  15. van der Wal, C. H. et al. Quantum superposition of macroscopic persistent-current states. Science 290, 773–777 (2000)

    Article  ADS  CAS  Google Scholar 

  16. Pashkin, Y. A. et al. Quantum oscillations in two coupled charge qubits. Nature 421, 823–826 (2003)

    Article  ADS  CAS  Google Scholar 

  17. Chiorescu, I., Nakmura, Y., Harmans, C. J. P. M. & Mooji, J. E. Coherent quantum dynamics of a superconducting flux qubit. Science 299, 1869–1871 (2003)

    Article  ADS  CAS  Google Scholar 

  18. Hoekstra, H. F. T. et al. General features of quantum creep in high- Tc superconductors. Phys. Rev. Lett. 80, 4293–4296 (1998)

    Article  ADS  CAS  Google Scholar 

  19. Nicodemi, M. & Jensen, H. J. Creep of superconducting vortices in the limit of vanishing temperature: A fingerprint of off-equilibrium dynamics. Phys. Rev. Lett. 86, 4378–4381 (2001)

    Article  ADS  CAS  Google Scholar 

  20. van der Zant, H. S. J., Fritschy, J. F. C., Orlando, T. P. & Mooij, J. E. Dynamics of vortices in underdamped Josephson-junction arrays. Phys. Rev. Lett. 66, 531–2534 (1991)

    Article  Google Scholar 

  21. Tighe, T. S., Johnson, A. T. & Tinkham, M. Vortex motion in two-dimensional arrays of small, underdamped Josephson junctions. Phys. Rev. B 44, 10286–10290 (1991)

    Article  ADS  CAS  Google Scholar 

  22. Ustinov, A. V. Solitons in Josephson junctions. Physica D 123, 315–329 (1998)

    Article  ADS  Google Scholar 

  23. Kato, T. & Imada, M. Macroscopic quantum tunneling of a fluxon in a long Josephson junction. J. Phys. Soc. Jpn 65, 2963–2975 (1996)

    Article  ADS  CAS  Google Scholar 

  24. Shnirman, A., Ben-Jacob, E. & Malomed, B. A. Tunneling and resonant tunneling of fluxons in a long Josephson junction. Phys. Rev. B 56, 14677–14685 (1997)

    Article  ADS  CAS  Google Scholar 

  25. Koval, Y. et al. Narrow long Josephson junctions. IEEE Trans. Appl. Supercond. 9, 3957–3961 (1999)

    Article  ADS  Google Scholar 

  26. McLaughlin, D. W. & Scott, A. C. Perturbation analysis of fluxon dynamics. Phys. Rev. A 18, 1652–1980 (1978)

    Article  ADS  Google Scholar 

  27. Grønbech-Jensen, N., Lomdahl, P. & Samuelsen, M. Phase locking of long annular Josephson junctions coupled to an external rf magnetic field. Phys. Lett. A 154, 14–18 (1991)

    Article  ADS  Google Scholar 

  28. Ustinov, A. V. & Thyssen, N. Experimental study of fluxon dynamics in a harmonic potential well. J. Low Temp. Phys. 106, 193–200 (1997)

    Article  ADS  CAS  Google Scholar 

  29. Fulton, T. A. & Dunkleberger, L. N. Lifetime of the zero-voltage state in Josephson tunnel junctions. Phys. Rev. B 9, 4760–4768 (1974)

    Article  ADS  CAS  Google Scholar 

  30. Wallraff, A. et al. Switching current measurements of large area Josephson tunnel junctions. Rev. Sci. Instrum 74, 3740–3748 (2003)

    Article  ADS  CAS  Google Scholar 

  31. Wallraff, A., Duty, T., Lukashenko, A. & Ustinov, A. V. Multi-photon transitions between energy levels in a current-biased Josephson tunnel junction. Phys. Rev. Lett. 90, 037003 (2003)

    Article  ADS  CAS  Google Scholar 

  32. Wallraff, A., Koval, Y., Levitchev, M., Fistul, M. V. & Ustinov, A. V. Annular long Josephson junctions in a magnetic field: Engineering and probing the fluxon potential. J. Low Temp. Phys. 118, 543–553 (2000)

    Article  ADS  CAS  Google Scholar 

  33. Kemp, A., Wallraff, A. & Ustinov, A. V. Josephson vortex qubit: Design, preparation and read-out. Phys. Status Solidi B 233, 472–481 (2002)

    Article  ADS  CAS  Google Scholar 

  34. Martucciello, N. et al. Fluxon dynamics in long annular Josephson tunnel junctions. Phys. Rev. B 57, 5444–5449 (1998)

    Article  ADS  CAS  Google Scholar 

Download references


We thank G. Blatter, T. Kato, G. Schön and S. Shnirman for discussions. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG).

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. Wallraff.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wallraff, A., Lukashenko, A., Lisenfeld, J. et al. Quantum dynamics of a single vortex. Nature 425, 155–158 (2003).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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