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:

Preparing topological states of a Bose–Einstein condensate

Nature volume 401, pages 568–572 (1999)Cite this article

Abstract

Observations of Bose–Einstein condensates—macroscopic populations of ultracold atoms occupying a single quantum state—in dilute alkali-metal and hydrogen gases have stimulated a great deal of research into the statistical physics of weakly interacting quantum degenerate systems1,2. Recent experiments offer a means of exploring fundamental low-temperature physics in a controllable manner. A current experimental goal in the study of trapped Bose gases is the observation of superfluid-like behaviour, analogous to the persistent currents seen in superfluid liquid helium which flow without observable viscosity. The ‘super’ properties of Bose-condensed systems occur because the macroscopic occupation of a quantized mode provides a stabilizing mechanism that inhibits decay through thermal relaxation3. Here we show how to selectively generate superfluid vortex modes with different angular momenta in a Bose–Einstein condensate. Our approach involves solving the time-dependent equation of motion of a two-component condensate with strongly coupled internal atomic states, as recently investigated experimentally4,5. The generation of vortices relies on the coupling between the states (achieved by applying an electromagnetic field), combined with mechanical rotation of the trapping potentials which confine the condensate.

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: Method for creating a vortex.
Figure 2: Dynamical evolution to a vortex.
Figure 3: Unit vortex preparation.
Figure 4: Double and triple vortex preparation.
Figure 5: Dipole and quadrupole preparation.

Similar content being viewed by others

References

  1. Cornell,E. A., Ensher,J. R. & Wieman, C. E. Experiments in dilute atomic Bose-Einstein condensation. In Proc. 1998 Enrico Fermi Summer School on Bose-Einstein Condensation (eds Inguscio, M., Stringari, S. & Wieman, C. E.) (SIF, Bologna, in the press); also as preprint cond-mat/9903109 at 〈http://xxx.lanl.gov〉 (1999).

    Google Scholar 

  2. Ketterle,W., Durfee,D. S. & Stamper-Kurn, D. M. Making, probing and understanding Bose-Einstein condensates. In Proc. 1998 Enrico Fermi Summer School on Bose-Einstein condensation (eds Inguscio, M., Stringari, S. & Wieman, C. E.) (SIF, Bologna, in the press); also as preprint cond-mat/9904034 at 〈http://xxx.lanl.gov〉 (1999).

    Google Scholar 

  3. Leggett,A. in The New Physics (ed. Davies, P.) 268–288 (Cambridge Univ. Press, New York, 1989).

    Book  Google Scholar 

  4. Matthews,M. R. et al. Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose-Einstein condensate. Phys. Rev. Lett. (in the presss); also as preprint cond-mat/9906288 at 〈http://xxx.lanl.gov〉 (1999).

  5. Williams,J., Walser,R., Cooper,J., Cornell,E. A. & Holland, M. Excitation of an antisymmetric collective mode in a strongly coupled two-component Bose-Einstein condensate. Preprint cond-mat/9904399 at 〈http://xxx.lanl.gov〉 (1999).

  6. Anderson,M. H., Ensher,J. R., Matthews,M. R., Wieman,C. E. & Cornell,E. A. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198 –201 (1995).

    Article  ADS  CAS  Google Scholar 

  7. Davis,K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).

    Article  ADS  CAS  Google Scholar 

  8. Bradley,C. C., Sackett,C. A., Tollet,J. J. & Hulet,R. G. Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions. Phys. Rev. Lett. 75, 1687– 1690 (1995); Erratum. Phys. Rev. Lett. 79, 1170–1170 ( 1997).

    Article  ADS  CAS  Google Scholar 

  9. Butts,D. A. & Rokhsar,D. S. Predicting signatures of rotating Bose-Einstein condensates. Nature 397, 327 –329 (1999).

    Article  ADS  CAS  Google Scholar 

  10. Rokhsar,D. S. Vortex stability and persistent currents in trapped Bose gases. Phys. Rev. Lett. 79, 2164–2167 (1997).

    Article  ADS  CAS  Google Scholar 

  11. Dalfovo,F. & Stringari,S. Bosons in anisotropic traps: Ground state and vortices. Phys. Rev. A 53, 2477 –2485 (1996).

    Article  ADS  CAS  Google Scholar 

  12. Ho,T.-L. & Shenoy,V. B. Local spin-gauge symmetry of the Bose-Einstein condensates in atomic gases. Phys. Rev. Lett. 77, 2595–2599 (1996).

    Article  ADS  CAS  Google Scholar 

  13. Barenghi,C. F. Vortex waves in a cloud of Bose-Einstein-condensed, trapped alkali-metal atoms. Phys. Rev. A 54, 5445– 5446 (1996).

    Article  ADS  CAS  Google Scholar 

  14. Fetter,A. L. Vortex stability in a trapped Bose condensate. J. Low Temp. Phys. 113, 189–194 ( 1998).

    Article  ADS  CAS  Google Scholar 

  15. Feder,D. L., Clark,C. W. & Schneider, B. I. Vortex stability of interacting Bose-Einstein condensates confined in anisotropic harmonic traps. Phys. Rev. Lett. 82, 4956–4959 (1999).

    Article  ADS  CAS  Google Scholar 

  16. Caradoc-Davis, B. M., Ballagh, R. J. & Burnett, K. Coherent dynamics of vortex formation in trapped Bose-Einstein condensates. Phys. Rev. Lett. 83, 895– 898 (1999).

    Article  ADS  Google Scholar 

  17. Dodd,R. J., Burnett,K., Edwards,M. & Clark,C. W. Excitation spectroscopy of vortex states in dilute Bose-Einstein condensed gases. Phys. Rev. A 56, 587–590 ( 1997).

    Article  ADS  CAS  Google Scholar 

  18. Marzlin,K.-P. & Zhang,W. Vortex coupler for atomic Bose-Einstein condensates. Phys. Rev. Lett. 79, 4728– 4731 (1997).

    Article  ADS  CAS  Google Scholar 

  19. Bolda,E. L. & Walls,D. F. Creation of vortices in a Bose-Einstein condensate by a Raman technique. Phys. Lett. A 246, 32–36 (1998).

    Article  ADS  CAS  Google Scholar 

  20. Dum,R., Cirac,J. I., Lewenstein,M. & Zoller,P. Creation of dark solitons and vortices in Bose-Einstein condensates. Phys. Rev. Lett. 80, 2972–2975 (1998).

    Article  ADS  CAS  Google Scholar 

  21. Lifshitz,E. M. & Pitaevskii,L. P. Statistical Physics (Pergamon, Oxford, 1980).

  22. Holland,M. J., Jin,D. S., Chiofalo,M. L. & Cooper,J. Emergence of interaction effects in Bose-Einstein condensation. Phys. Rev. Lett. 78, 3801–3805 (1997).

    Article  ADS  CAS  Google Scholar 

  23. Williams,J. E. The Preparation of Topological Modes in a Strongly-Coupled Two-Component Bose-Einstein Condensate. Thesis, Univ. Colorado (1999).

    Google Scholar 

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

    Google Scholar 

  25. 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 

Download references

Acknowledgements

We thank E. A. Cornell, M. R. Matthews, P. C. Haljan, B P. Anderson and C. E. Wieman for discussions on the realization of our scheme, and R. Walser and J. Cooper for comments. This work was supported by the National Science Foundation.

Author information

Authors and Affiliations

  1. JILA and Physics Department, University of Colorado, Boulder, 80309-0440, Colorado, USA

    J. E. Williams & M. J. Holland

Authors
  1. J. E. Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. J. Holland
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. J. Holland.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Williams, J., Holland, M. Preparing topological states of a Bose–Einstein condensate. Nature 401, 568–572 (1999). https://doi.org/10.1038/44095

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/44095

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