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:

Spontaneous vortices in the formation of Bose–Einstein condensates

Nature volume 455, pages 948–951 (2008)Cite this article

Abstract

Phase transitions are ubiquitous in nature, and can be arranged into universality classes such that systems having unrelated microscopic physics show identical scaling behaviour near the critical point. One prominent universal element of many continuous phase transitions is the spontaneous formation of topological defects during a quench through the critical point1,2,3. The microscopic dynamics of defect formation in such transitions are generally difficult to investigate, particularly for superfluids4,5,6,7. However, Bose–Einstein condensates (BECs) offer unique experimental and theoretical opportunities for probing these details. Here we present an experimental and theoretical study of the BEC phase transition of a trapped atomic gas, in which we observe and statistically characterize the spontaneous formation of vortices during condensation8,9. Using microscopic theories10,11,12,13,14,15,16,17 that incorporate atomic interactions and quantum and thermal fluctuations of a finite-temperature Bose gas, we simulate condensation and observe vortex formation in close quantitative agreement with our experimental results. Our studies provide further understanding of the development of coherence in superfluids, and may allow for direct investigation of universal phase transition dynamics.

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: Schematic of spontaneous vortex formation.
Figure 2: Condensate formation and vorticity.
Figure 3: Vortices in the harmonic and toroidal traps.
Figure 4: BEC growth dynamics.

Similar content being viewed by others

References

  1. Kibble, T. W. B. Topology of cosmic domains and strings. J. Phys. A 9, 1387–1398 (1976)

    Article  ADS  Google Scholar 

  2. Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985)

    Article  ADS  CAS  Google Scholar 

  3. Zurek, W. H. Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177–221 (1996)

    Article  ADS  CAS  Google Scholar 

  4. Hendry, P. C., Lawson, N. S., Lee, R., McClintock, P. V. E. & Williams, C. D. H. Generation of defects in superfluid 4He as an analogue of the formation of cosmic strings. Nature 368, 315–317 (1994)

    Article  ADS  CAS  Google Scholar 

  5. Ruutu, V. M. H. et al. Vortex formation in neutron-irradiated superfluid 3He as an analogue of cosmological defect formation. Nature 382, 334–336 (1996)

    Article  ADS  CAS  Google Scholar 

  6. Baüerle, C., Bunkov, Y. M., Fisher, S. N., Godfrin, H. & Pickett, G. R. Laboratory simulation of cosmic string formation in the early Universe using superfluid 3He. Nature 382, 332–334 (1996)

    Article  ADS  Google Scholar 

  7. Dodd, M., Hendry, P., Lawson, N., McClintock, P. & Williams, C. Nonappearance of vortices in the fast mechanical expansions of liquid 4He through the Lambda transition. Phys. Rev. Lett. 81, 3703–3706 (1998)

    Article  ADS  CAS  Google Scholar 

  8. Anglin, J. R. & Zurek, W. H. Vortices in the wake of rapid Bose–Einstein condensation. Phys. Rev. Lett. 83, 1707–1710 (1999)

    Article  ADS  CAS  Google Scholar 

  9. Svistunov, B. V. Strongly non-equilibrium Bose–Einstein condensation in a trapped gas. Phys. Lett. A 287, 169–174 (2001)

    Article  ADS  CAS  Google Scholar 

  10. Stoof, H. T. C. Coherent versus incoherent dynamics during Bose–Einstein condensation in atomic gases. J. Low Temp. Phys. 114, 11–108 (1999)

    Article  ADS  CAS  Google Scholar 

  11. Davis, M. J., Ballagh, R. J. & Burnett, K. Dynamics of thermal Bose fields in the classical limit. J. Phys. B 34, 4487–4512 (2001)

    Article  ADS  CAS  Google Scholar 

  12. Davis, M. J., Morgan, S. A. & Burnett, K. Simulations of Bose fields at finite temperature. Phys. Rev. Lett. 87, 160402 (2001)

    Article  ADS  CAS  Google Scholar 

  13. Gardiner, C. W., Anglin, J. R. & Fudge, T. I. A. The stochastic Gross–Pitaevskii equation. J. Phys. B 35, 1555–1582 (2002)

    Article  ADS  CAS  Google Scholar 

  14. Gardiner, C. W. & Davis, M. J. The stochastic Gross–Pitaevskii equation: II. J. Phys. B 36, 4731–4753 (2003)

    Article  ADS  CAS  Google Scholar 

  15. Blakie, P. B. & Davis, M. J. Projected Gross–Pitaevskii equation for harmonically confined Bose gases at finite temperature. Phys. Rev. A 72, 063608 (2005)

    Article  ADS  Google Scholar 

  16. Davis, M. J. & Blakie, P. B. Critical temperature of a trapped Bose gas: Comparison of theory and experiment. Phys. Rev. Lett. 96, 060404 (2006)

    Article  ADS  Google Scholar 

  17. Bradley, A. S., Gardiner, C. W. & Davis, M. J. Bose–Einstein condensation from a rotating thermal cloud: Vortex nucleation and lattice formation. Phys. Rev. A 77, 033616 (2008)

    Article  ADS  Google Scholar 

  18. Svistunov, B. V. Highly nonequilibrium Bose condensation in a weakly interacting gas. J. Mosc. Phys. Soc. 1, 373–390 (1991)

    Google Scholar 

  19. Kagan, Y., Svistunov, B. V. & Shlyapnikov, G. V. The Bose-condensation kinetics in an interacting Bose–gas. Zh. Eksp. Teor. Fiz. [Sov. Phys. JETP 75, 387 (1992)] 101, 528–539 (1992)

    Google Scholar 

  20. Kagan, Y. & Svistunov, B. V. Kinetics of long-range order formation in Bose-condensation in interacting gas. Zh. Eksp. Teor. Fiz. [Sov. Phys. JETP 78, 187 (1994)] 105, 353–367 (1994)

    Google Scholar 

  21. Kagan, Y. & Svistunov, B. V. Evolution of correlation properties and appearance of broken symmetry in the process of Bose–Einstein condensation. Phys. Rev. Lett. 79, 3331–3334 (1997)

    Article  ADS  CAS  Google Scholar 

  22. Berloff, N. G. & Svistunov, B. V. Scenario of strongly nonequilibrated Bose–Einstein condensation. Phys. Rev. A 66, 013603 (2002)

    Article  ADS  Google Scholar 

  23. Scherer, D. R., Weiler, C. N., Neely, T. W. & Anderson, B. P. Vortex formation by merging of multiple trapped Bose–Einstein condensates. Phys. Rev. Lett. 98, 110402 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  25. 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 

  26. Davis, M. J. & Gardiner, C. W. Growth of a Bose–Einstein condensate: a detailed comparison of theory and experiment. J. Phys. B 35, 733–742 (2002)

    Article  ADS  CAS  Google Scholar 

  27. Pethick, C. & Smith, H. Bose–Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2002)

    Google Scholar 

  28. Ryu, C. et al. Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap. Phys. Rev. Lett. 99, 260401 (2007)

    Article  ADS  CAS  Google Scholar 

  29. Sadler, L. E., Higbie, J. M., Leslie, S. R., Vengalattaore, M. & Stamper-Kurn, D. M. Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate. Nature 443, 312–315 (2006)

    Article  ADS  CAS  Google Scholar 

  30. Petrich, W., Anderson, M., Ensher, J. & Cornell, E. Stable, tightly confining magnetic trap for evaporative cooling of neutral atoms. Phys. Rev. Lett. 74, 3352–3355 (1995)

    Article  ADS  CAS  Google Scholar 

  31. Chevy, F., Madison, K. W. & Dalibard, J. Measurement of the angular momentum of a rotating Bose–Einstein condensate. Phys. Rev. Lett. 85, 2223–2227 (2000)

    Article  ADS  CAS  Google Scholar 

  32. Haljan, P. C., Anderson, B. P., Coddington, I. & Cornell, E. A. Use of surface-wave spectroscopy to characterize tilt modes of a vortex in a Bose–Einstein condensate. Phys. Rev. Lett. 86, 2922–2925 (2001)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank D. Roberts, B. Svistunov, E. Wright and W. Zurek for discussions. The experimental work was financially supported by the US National Science Foundation under grant no. 0354977, and by the Army Research Office. The theoretical work was financially supported by the Australian Research Council Centre of Excellence for Quantum-Atom Optics and the University of Queensland.

Author information

Author notes

  1. Ashton S. Bradley

    Present address: Present address: Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, PO Box 56, Dunedin, New Zealand.,

Authors and Affiliations

  1. College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA ,

    Chad N. Weiler, Tyler W. Neely, David R. Scherer & Brian P. Anderson

  2. ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Queensland 4072, Australia ,

    Ashton S. Bradley & Matthew J. Davis

Authors
  1. Chad N. Weiler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tyler W. Neely
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David R. Scherer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ashton S. Bradley
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Matthew J. Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Brian P. Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brian P. Anderson.

Supplementary information

Supplementary Information

This file contains a Supplementary Discussion, Supplementary Figures 1 and 2 with Legends, Supplementary Table 1, Supplementary Notes and Supplementary Video Legends 1-10 (PDF 369 kb)

Supplementary Video 1

Supplementary Video 1 shows a condensate formation in a harmonic trap with no resulting vortices. (MOV 2176 kb)

Supplementary Video 2

Supplementary Video 2 shows a condensate formation in a harmonic trap resulting in a single vortex that remains near trap centre. (MOV 2184 kb)

Supplementary Video 3

Supplementary Video 3 shows a condensate formation in a harmonic trap with three vortices at early times, two of which damp to leave one vortex at long times that is not vertically aligned. (MOV 2180 kb)

Supplementary Video 4

Supplementary Video 4 shows a condensate formation in a harmonic trap resulting in two oppositely charged vortices that precess about the centre in opposite directions. (MOV 2199 kb)

Supplementary Video 5

Supplementary Video 5 shows a condensate formation in a harmonic trap showing complicated vortex dynamics with flips of orientation and vortex reconnections. (MOV 2238 kb)

Supplementary Video 6

Supplementary Video 6 shows a condensate formation in a toroidal trap resulting in a single vortex that is trapped as a persistent current by the central barrier. (MOV 2213 kb)

Supplementary Video 7

Supplementary Video 7 shows a of condensate formation in a toroidal trap resulting in a persistent current with an additional vortex precessing about the central barrier (MOV 2215 kb)

Supplementary Video 8

Supplementary Video 8 shows of condensate formation in a toroidal trap with no resulting persistent current but a single vortex precessing about the centre. (MOV 2234 kb)

Supplementary Video 9

Supplementary Video 9 shows a of condensate formation in a toroidal trap with two vortices of the same charge, one of which is trapped on the central barrier. (MOV 2263 kb)

upplementary Video 10

Supplementary Video 10 shows a of condensate formation in a toroidal trap resulting in a doubly-charged persistent current. (MOV 2232 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weiler, C., Neely, T., Scherer, D. et al. Spontaneous vortices in the formation of Bose–Einstein condensates. Nature 455, 948–951 (2008). https://doi.org/10.1038/nature07334

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature07334

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