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.

  • Letter
  • Published:

Skyrmions in a ferromagnetic Bose–Einstein condensate

Nature volume 411, pages 918–920 (2001)Cite this article

Abstract

Multi-component Bose–Einstein condensates1,2,3 provide opportunities to explore experimentally the wealth of physics associated with the spin degrees of freedom4,5,6,7. The ground-state properties8,9,10,11 and line-like vortex excitations8,12,13 of these quantum systems have been studied theoretically. In principle, nontrivial spin textures consisting of point-like topological excitations, or skyrmions14,15, could exist in a multi-component Bose–Einstein condensate, owing to the superfluid nature of the gas. Although skyrmion excitations are already known in the context of nuclear physics and the quantum-Hall effect, creating these excitations in an atomic condensate would offer an opportunity to study their physical behaviour in much greater detail, while also enabling an ab initio comparison between theory and experiment. Here we investigate theoretically the stability of skyrmions in a fictitious spin-1/2 condensate of 87Rb atoms. We find that skyrmions can exist in such a gas only as a metastable state, but with a lifetime comparable to (or even longer than) the typical lifetime of the condensate itself.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Decay rate Γ and size λ (inset) of the skyrmion as a function of the number of atoms trapped in the core.
Figure 2: The average spin texture of the skyrmion.
Figure 3: The potential barrier produced by the skyrmion texture.

Similar content being viewed by others

References

  1. Myatt, C. J., Burt, E. A., Ghrist, R. W., Cornell, E. A. & Wieman, C. E. Production of two overlapping Bose–Einstein condensates by sympathetic cooling. Phys. Rev. Lett. 78, 586–589 (1997).

    Article  ADS  CAS  Google Scholar 

  2. Stamper-Kurn, D. M. et al. Optical confinement of a Bose–Einstein condensate. Phys. Rev. Lett. 80, 2027–2030 (1998).

    Article  ADS  CAS  Google Scholar 

  3. Stenger, J. et al. Spin domains in ground-state Bose–Einstein condensates. Nature 396, 345–348 (1998).

    Article  ADS  CAS  Google Scholar 

  4. Hall, D. S., Matthews, M. R., Ensher, J. R., Wieman, C. E. & Cornell, E. A. Dynamics of component separation in a binary mixture of Bose–Einstein condensates. Phys. Rev. Lett. 81, 1539–1542 (1998).

    Article  ADS  CAS  Google Scholar 

  5. Stamper-Kurn, D. M. et al. Quantum tunneling across spin domains in a Bose condensate. Phys. Rev. Lett. 83, 661–664 (1999).

    Article  ADS  CAS  Google Scholar 

  6. Matthews, M. R. et al. Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose–Einstein condensate. Phys. Rev. Lett. 83, 3358–3361 (1999).

    Article  ADS  CAS  Google Scholar 

  7. Matthews, M. R. et al. Vortices in a Bose–Einstein condensate. Phys. Rev. Lett. 83, 2498–2501 (1999).

    Article  ADS  CAS  Google Scholar 

  8. Ho, T.-L. Spinor Bose condensates in optical traps. Phys. Rev. Lett. 81, 742–745 (1998).

    Article  ADS  CAS  Google Scholar 

  9. Ohmi, T. & Machida, K. Bose–Einstein condensation with internal degrees of freedom in alkali atom gases. J. Phys. Soc. Jpn 67, 1822–1825 (1998).

    Article  ADS  CAS  Google Scholar 

  10. Law, C. K., Pu, H. & Bigelow, N. B. Quantum spins mixing in spin Bose–Einstein condensates. Phys. Rev. Lett. 81, 5257–5261 (1998).

    Article  ADS  CAS  Google Scholar 

  11. Ho, T.-L. & Yip, S.-K. Fragmented and single condensate ground states of spin-1 Bose gas. Phys. Rev. Lett. 84, 4031–4034 (2000).

    Article  ADS  CAS  Google Scholar 

  12. Yip, S.-K. Internal vortex structure of a trapped spinor Bose–Einstein condensate. Phys. Rev. Lett. 83, 4677–4681 (1999).

    Article  ADS  CAS  Google Scholar 

  13. Williams, J. E. & Holland, M. J. Preparing topological states of a Bose–Einstein condensate. Nature 401, 568–572 (1999).

    Article  ADS  CAS  Google Scholar 

  14. Skyrme, T. H. R. A non-linear field theory. Proc. R. Soc. Lond. A 260, 127–138 (1961).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  15. Skyrme, T. H. R. A unified field theory of mesons and baryons. Nucl. Phys. 31, 556–569 (1962).

    Article  MathSciNet  CAS  Google Scholar 

  16. Julienne, P. S., Mies, F. H., Tiesinga, E. & Williams, C. J. Collisional stability of double Bose condensates. Phys. Rev. Lett. 78, 1880–1883 (1997).

    Article  ADS  CAS  Google Scholar 

  17. Côté, R. et al. Collective excitations, NMR, and phase transitions in Skyrme crystals. Phys. Rev. Lett. 78, 4825–4828 (1997).

    Article  ADS  Google Scholar 

  18. Madison, K. W., Chevy, F., Wohlleben, W. & Dalibard, J. Vortex formation in a stirred Bose–Einstein condensate. Phys. Rev. Lett. 84, 806–809 (2000).

    Article  ADS  CAS  Google Scholar 

  19. Stoof, H. T. C. Macroscopic quantum tunneling of a Bose–Einstein condensate. J. Stat. Phys. 87, 1353–1366 (1997).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank M. Bijlsma for help in the numerical calculations and for helpful remarks. We also thank J. Anglin, G. 't Hooft, D. Olive and J. Smit for useful discussions. This work is supported by the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Utrecht, Princetonplein 5, Utrecht, 3584 CC, The Netherlands

    Usama Al Khawaja & Henk Stoof

Authors
  1. Usama Al Khawaja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Henk Stoof
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Usama Al Khawaja.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Al Khawaja, U., Stoof, H. Skyrmions in a ferromagnetic Bose–Einstein condensate. Nature 411, 918–920 (2001). https://doi.org/10.1038/35082010

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/35082010

This article is cited by

Comments

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.

Search

Advanced 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