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.

  • Article
  • Published:

Observation of an Efimov spectrum in an atomic system

This article has been updated

Abstract

In 1970, Vitaly Efimov predicted that three quantum particles subjected to a resonant pair-wise interaction can join into an infinite number of loosely bound states, even if each pair of particles cannot bind. The properties of these aggregates, such as the peculiar geometric scaling of their energy spectrum, are universal, that is, independent of the microscopic details of their components. Despite an extensive search in many different physical systems, including atoms, molecules and nuclei, the characteristic spectrum of Efimov trimer states has not been observed so far. Here, we report on the discovery of two bound trimer states of potassium atoms very close to the Efimov scenario, which we reveal by studying three-particle collisions in an ultracold gas. Our observation provides the first evidence of an Efimov spectrum and enables a direct test of its scaling behaviour, providing potentially general insights into the physics of few-body systems.

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: Efimov spectrum.
Figure 2: Atom–dimer resonances at a>0.

Similar content being viewed by others

Change history

  • 16 July 2009

    In the version of this article originally published online, a correction was needed to Fig. 1a, where E2 should have read E2 . This correction has now been made in all versions of the article.

References

  1. Burnett, K., Julienne, P. S., Lett, P. D., Tiesinga, E. & Williams, C. J. Quantum encounters of the cold kind. Nature 416, 225–232 (2002).

    Article  ADS  Google Scholar 

  2. Köhler, T., Goral, K. & Julienne, P. Production of cold molecules via magnetically tunable Feshbach resonances. Rev. Mod. Phys. 78, 1311–1361 (2006).

    Article  ADS  Google Scholar 

  3. Jensen, A. S., Riisager, K., Fedorov, D. V. & Garrido, E. Structure and reactions of quantum halos. Rev. Mod. Phys. 76, 215–261 (2004).

    Article  ADS  Google Scholar 

  4. Efimov, V. Weakly-bound states of three resonantly-interacting particles. Sov. J. Nucl. Phys. 12, 589–595 (1971).

    Google Scholar 

  5. Efimov, V. Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B 33, 563–564 (1970).

    Article  ADS  Google Scholar 

  6. Thomas, L. H. The interaction between a neutron and a proton in the structure of H3. Phys. Rev. 47, 903–909 (1935).

    Article  ADS  Google Scholar 

  7. Efimov, V. Energy levels of three resonantly interacting particles. Nucl. Phys. A 210, 157–188 (1973).

    Article  ADS  Google Scholar 

  8. Brühl, R. et al. Matter wave diffraction from an inclined transmission grating: Searching for the elusive 4He trimer Efimov state. Phys. Rev. Lett. 95, 063002 (2005).

    Article  ADS  Google Scholar 

  9. Kraemer, T. et al. Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 315–318 (2006).

    Article  ADS  Google Scholar 

  10. Knoop, S. et al. Observation of an Efimov-like resonance in ultracold atom-dimer scattering. Nature Phys. 5, 227–230 (2009).

    Article  ADS  Google Scholar 

  11. Tiesinga, E., Verhaar, B. J. & Stoof, H. T. C. Threshold and resonance phenomena in ultracold ground-state collisions. Phys. Rev. A 47, 4114–4122 (1993).

    Article  ADS  Google Scholar 

  12. Ottenstein, T. B., Lompe, T., Kohnen, M., Wenz, A. N. & Jochim, S. Collisional stability of a three-component degenerate Fermi gas. Phys. Rev. Lett. 101, 203202 (2008).

    Article  ADS  Google Scholar 

  13. Huckans, J. H., Williams, J. R., Hazlett, E. L., Stites, R. W. & O’Hara, K. M. Three-body recombination in a three-state Fermi gas with widely tunable interactions. Phys. Rev. Lett. 102, 165302 (2009).

    Article  ADS  Google Scholar 

  14. Barontini, G. et al. Observation of heteronuclear atomic Efimov resonances. Preprint at <http://arxiv.org/abs/0901.4584> (2009).

  15. D’Incao, J. P., Suno, H. & Esry, B. D. Limits on universality in ultracold three boson recombination. Phys. Rev. Lett. 93, 123201 (2004).

    Article  ADS  Google Scholar 

  16. Braaten, E. & Hammer, H.-W. Efimov physics in cold atoms. Ann. Phys. 322, 120–163 (2007).

    Article  ADS  Google Scholar 

  17. Bedaque, P. F., Braaten, E. & Hammer, H. W. Three body recombination in Bose gases with large scattering length. Phys. Rev. Lett. 85, 908–911 (2000).

    Article  ADS  Google Scholar 

  18. Petrov, D. S. Three-boson problem near a narrow Feshbach resonance. Phys. Rev. Lett. 93, 143201 (2004).

    Article  ADS  Google Scholar 

  19. Esry, B. D., Greene, C. H. & Burke, J. P. Jr Recombination of three atoms in the ultracold limit. Phys. Rev. Lett. 83, 1751–1754 (1999).

    Article  ADS  Google Scholar 

  20. Fedichev, P. O., Reynolds, M. W. & Shlyapnikov, G. V. Three-body recombination of ultracold atoms to a weakly bound s level. Phys. Rev. Lett. 77, 2921–2924 (1996).

    Article  ADS  Google Scholar 

  21. Weber, T. et al. Three-body recombination at large scattering lengths in an ultracold atomic gas. Phys. Rev. Lett. 91, 123201 (2004).

    Article  ADS  Google Scholar 

  22. Nielsen, E. & Macek, J. H. Low-energy recombination of identical bosons by three-body collisions. Phys. Rev. Lett. 83, 1566–1569 (1999).

    Article  ADS  Google Scholar 

  23. Massignan, P. & Stoof, H. Efimov states near a Feshbach resonance. Phys. Rev. A 78, 030701(R) (2008).

    Article  ADS  Google Scholar 

  24. D’Incao, J. P., Greene, C. H. & Esry, B. D. The short-range three-body phase and other issues impacting the observation of Efimov physics in ultracold quantum gases. J. Phys. B 4, 044016 (2009).

    Article  ADS  Google Scholar 

  25. Hammer, H.-W. & Platter, L. Universal properties of the four-body system with large scattering length. Eur. Phys. J. A 32, 113–120 (2007).

    Article  ADS  Google Scholar 

  26. von Stecher, J., D’Incao, J. P. & Greene, C. H. Signatures of universal four-body phenomena and their relation to the Efimov effect. Nature Phys. 5, 417–421 (2009).

    Article  ADS  Google Scholar 

  27. Ferlaino, F. et al. Evidence for universal four-body states tied to an Efimov trimer. Phys. Rev. Lett. 102, 140401 (2009).

    Article  ADS  Google Scholar 

  28. D’Errico, C. et al. Feshbach resonances in ultracold 39K. New J. Phys. 9, 223 (2007).

    Article  ADS  Google Scholar 

  29. Roati, G. et al. 39K Bose–Einstein condensate with tunable interactions. Phys. Rev. Lett. 99, 010403 (2007).

    Article  ADS  Google Scholar 

  30. Fattori, M. et al. Magnetic dipolar interaction in a Bose–Einstein condensate atomic interferometer. Phys. Rev. Lett. 101, 190405 (2008).

    Article  ADS  Google Scholar 

  31. Schuster, J. et al. Avalanches in a Bose–Einstein condensate. Phys. Rev. Lett. 87, 170404 (2001).

    Article  ADS  Google Scholar 

  32. Platter, L., Ji, C. & Phillips, D. R. Range corrections to three-body observables near a Feshbach resonance. Phys. Rev. A 79, 022702 (2009).

    Article  ADS  Google Scholar 

  33. Thøgersen, M., Fedorov, D. V. & Jensen, A. S. Universal properties of Efimov physics beyond the scattering length approximation. Phys. Rev. A 78, 020501 (2008).

    Article  ADS  Google Scholar 

  34. Hammer, H.-W., Lähde, T. A. & Platter, L. Effective-range corrections to three-body recombination for atoms with large scattering length. Phys. Rev. A 75, 032715 (2007).

    Article  ADS  Google Scholar 

  35. Burt, E. A. et al. Coherence, correlations, and collisions: What one learns about Bose–Einstein condensates from their decay. Phys. Rev. Lett. 79, 337–340 (1997).

    Article  ADS  Google Scholar 

  36. Greene, C. H., Esry, B. D. & Suno, A. A revised formula for 3-body recombination that cannot exceed the unitarity limit. Nucl. Phys. A 737, 119–124 (2004).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank P. Massignan and H. Stoof for motivating this work and for discussions. We acknowledge also B. D. Esry, J. P. D’Incao, R. Grimm and co-workers, and A. Simoni for discussions. We are grateful to S. Bartalini and G. Thalhammer for technical help. This work has been supported by CNR within the EUROCORES Programme EuroQUAM of the European Science Foundation, by the European Research Council through the Starting Grant ‘QUPOL’ and by the Italian MIUR (PRIN2006 programme).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Zaccanti.

Supplementary information

Supplementary Information

Supplementary Information (PDF 353 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zaccanti, M., Deissler, B., D’Errico, C. et al. Observation of an Efimov spectrum in an atomic system. Nature Phys 5, 586–591 (2009). https://doi.org/10.1038/nphys1334

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1334

This article is cited by

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