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:

Universal van der Waals physics for three cold atoms near Feshbach resonances

Nature Physics volume 10, pages 768–773 (2014)Cite this article

Subjects

Abstract

Experimental studies with cold atoms have advanced our understanding of three-body physics, historically a fundamental yet challenging problem. This is because atomic interactions can be precisely varied in strength using magnetically tunable scattering resonances known as Feshbach resonances. Collisions near the unitarity limit, where scattering is maximum, are known to have universal aspects that are independent of short-range chemical details. Away from this limit, many quantum states are expected to be active during a three-body collision, making the collisional observables practically unpredictable. Here we predict three-body ultracold scattering rates by properly building in the pairwise van der Waals interactions plus the multi-spin properties of a tunable Feshbach resonance state characterized by known dimensionless two-body parameters. Numerically solving the Schrödinger equation then quantitatively determines three-atom collisional properties at all interaction strengths without needing adjustable parameters to fit data. Consequently, we can define a new class of van der Waals universality for cold atom three-body phenomena.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Figure 1: Three-body recombination length ρ3 for Cs atoms near the −11.7 G Feshbach resonance.
Figure 2: Atom–dimer relaxation rate β for Cs atoms near the 25 G Efimov resonance.
Figure 3: Three-body Efimov energy spectrum for Cs atoms near the −11.7 G Feshbach resonance.
Figure 4: Efimov physics for Cs atoms near the 554 G g-wave Feshbach resonance.
Figure 5: Three-body recombination loss rate L3 for85Rb atoms near the 155 G Feshbach resonance.

Similar content being viewed by others

References

  1. Levine, R. D. Molecular Reaction Dynamics (Cambridge Univ. Press, 2005).

    Book  Google Scholar 

  2. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010).

    Article  ADS  Google Scholar 

  3. 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 

  4. Berninger, M. et al. Universality of the three-body parameter for Efimov states in ultracold cesium. Phys. Rev. Lett. 107, 120401 (2011).

    Article  ADS  Google Scholar 

  5. Pollack, S. E., Dries, D. & Hulet, R. G. Universality in three- and four-body bound states of ultracold atoms. Science 326, 1683–1686 (2009).

    Article  ADS  Google Scholar 

  6. Gross, N., Shotan, Z., Kokkelmans, S. & Khaykovich, L. Observation of universality in ultracold 7Li three-body recombination. Phys. Rev. Lett. 103, 163202 (2009).

    Article  ADS  Google Scholar 

  7. Gross, N., Shotan, Z., Kokkelmans, S. & Khaykovich, L. Nuclear-spinindependent short-range three-body physics in ultracold atoms. Phys. Rev. Lett. 105, 103203 (2010).

    Article  ADS  Google Scholar 

  8. Wild, R. J., Makotyn, P., Pino, J. M., Cornell, E. A. & Jin, D. S. Measurements of Tan’s contact in an atomic Bose–Einstein condensate. Phys. Rev. Lett. 108, 145305 (2012).

    Article  ADS  Google Scholar 

  9. Braaten, E. & Hammer, H. W. Universality in few-body systems with large scattering length. Phys. Rep. 428, 259–390 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  10. Wang, Y., DIncao, J. P. & Esry, B. D. Ultracold few-body systems. Adv. At. Mol. Opt. Phys. 62, 1–115 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Delves, L. Tertiary and general-order collisions. Nucl. Phys. 9, 391–399 (1959).

    Article  Google Scholar 

  13. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Roy, S. et al. Test of the universality of the three-body Efimov parameter at narrow Feshbach resonances. Phys. Rev. Lett. 111, 053202 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Jona-Lasinio, M. & Pricoupenko, L. Three resonant ultracold bosons: Off-resonance effects. Phys. Rev. Lett. 104, 023201 (2010).

    Article  ADS  Google Scholar 

  19. Pricoupenko, L. Crossover in the Efimov spectrum. Phys. Rev. A 82, 043633 (2010).

    Article  ADS  Google Scholar 

  20. Sørensen, P., Fedorov, D., Jensen, A. & Zinner, N. T. Efimov physics and the three-body parameter within a two-channel framework. Phys. Rev. A 86, 052516 (2012).

    Article  ADS  Google Scholar 

  21. Sørensen, P. K., Fedorov, D., Jensen, A. & Zinner, N. T. Finite-range effects in energies and recombination rates of three identical bosons. J. Phys. B 46, 075301 (2013).

    Article  ADS  Google Scholar 

  22. Zinner, N. Efimov trimers near the zero-crossing of a Feshbach resonance. Few-Body Syst. 54, 597–603 (2013).

    Article  ADS  Google Scholar 

  23. Chin, C. Universal scaling of Efimov resonance positions in cold atom systems. Preprint at http://arxiv.org/abs/1111.1484 (2011).

  24. Schmidt, R., Rath, S. & Zwerger, W. Efimov physics beyond universality. Euro. Phys. J. B 85, 1–6 (2012).

    Article  Google Scholar 

  25. Wang, J., D’Incao, J. P., Esry, B. D. & Greene, C. H. Origin of the three-body parameter universality in Efimov physics. Phys. Rev. Lett. 108, 263001 (2012).

    Article  ADS  Google Scholar 

  26. Naidon, P., Endo, S. & Ueda, M. Physical origin of the universal three-body parameter in atomic Efimov physics. Preprint at http://arxiv.org/abs/1208.3912 (2012).

  27. Naidon, P., Endo, S. & Ueda, M. Microscopic origin and universality classes of the Efimov three-body parameter. Phys. Rev. Lett. 112, 105301 (2014).

    Article  ADS  Google Scholar 

  28. Mies, F. H., Tiesinga, E. & Julienne, P. S. Manipulation of Feshbach resonances in ultracold atomic collisions using time-dependent magnetic fields. Phys. Rev. A 61, 022721 (2000).

    Article  ADS  Google Scholar 

  29. Nygaard, N., Schneider, B. I. & Julienne, P. S. Two-channel R-matrix analysis of magnetic-field-induced Feshbach resonances. Phys. Rev. A 73, 042705 (2006).

    Article  ADS  Google Scholar 

  30. Jachymski, K. & Julienne, P. S. Analytical model of overlapping Feshbach resonances. Phys. Rev. A 88, 052701 (2013).

    Article  ADS  Google Scholar 

  31. Wang, Y. Universal Efimov Physics in Three- and Four-Body Collisions PhD thesis, Kansas State Univ. (2010).

  32. Gribakin, G. F. & Flambaum, V. V. Calculation of the scattering length in atomic collisions using the semiclassical approximation. Phys. Rev. A 48, 546–553 (1993).

    Article  ADS  Google Scholar 

  33. Gao, B. Solutions of the Schrödinger equation for an attractive 1/r6 potential. Phys. Rev. A 58, 1728–1734 (1998).

    Article  ADS  Google Scholar 

  34. Berninger, M. et al. Feshbach resonances, weakly bound molecular states, and coupled-channel potentials for cesium at high magnetic fields. Phys. Rev. A 87, 032517 (2013).

    Article  ADS  Google Scholar 

  35. Yamashita, M., Frederico, T. & Tomio, L. Three-boson recombination at ultralow temperatures. Phys. Lett. A 363, 468–472 (2007).

    Article  ADS  Google Scholar 

  36. Braaten, E., Hammer, H-W., Kang, D. & Platter, L. Three-body recombination of identical bosons with a large positive scattering length at nonzero temperature. Phys. Rev. A 78, 043605 (2008).

    Article  ADS  Google Scholar 

  37. Lee, M. D., Köhler, T. & Julienne, P. S. Excited Thomas–Efimov levels in ultracold gases. Phys. Rev. A 76, 012720 (2007).

    Article  ADS  Google Scholar 

  38. 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 42, 044016 (2009).

    Article  ADS  Google Scholar 

  39. Wang, J., D’Incao, J. P., Wang, Y. & Greene, C. H. Universal three-body recombination via resonant d-wave interactions. Phys. Rev. A 86, 062511 (2012).

    Article  ADS  Google Scholar 

  40. Huang, B., Sidorenkov, L. A., Grimm, R. & Hutson, J. M. Observation of the second triatomic resonance in Efimov’s scenario. Phys. Rev. Lett. 112, 190401 (2014).

    Article  ADS  Google Scholar 

  41. Zenesini, A. et al. Resonant atom-dimer collisions in cesium: Testing universality at positive scattering lengths. Preprint at http://arxiv.org/abs/1406.3443 (2014).

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

    Article  ADS  Google Scholar 

  43. Gogolin, A. O., Mora, C. & Egger, R. Analytical solution of the bosonic three-body problem. Phys. Rev. Lett. 100, 140404 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  44. Wang, Y., D’Incao, J. P. & Esry, B. D. Ultracold three-body collisions near narrow Feshbach resonances. Phys. Rev. A 83, 042710 (2011).

    Article  ADS  Google Scholar 

  45. Ferlaino, F. et al. Efimov resonances in ultracold quantum gases. Few-Body Syst. 51, 113–133 (2011).

    Article  ADS  Google Scholar 

  46. Wang, Y., D’Incao, J. P. & Greene, C. H. Universal three-body physics for fermionic dipoles. Phys. Rev. Lett. 107, 233201 (2011).

    Article  ADS  Google Scholar 

  47. Wang, Y., Wang, J., D’Incao, J. P. & Greene, C. H. Universal three-body parameter in heteronuclear atomic systems. Phys. Rev. Lett. 109, 243201 (2012).

    Article  ADS  Google Scholar 

  48. Tolstikhin, O. I., Watanabe, S. & Matsuzawa, M. ‘Slow’ variable discretization: A novel approach for Hamiltonians allowing adiabatic separation of variables. J. Phys. B 29, L389–L395 (1996).

    Article  ADS  Google Scholar 

  49. Kokoouline, V. & Greene, C. H. Unified theoretical treatment of dissociative recombination of D3h triatomic ions: Application to H3+ and D3+. Phys. Rev. A 68, 012703 (2003).

    Article  ADS  Google Scholar 

  50. Santra, R. & Cederbaum, L. S. Non-Hermitian electronic theory and applications to clusters. Phys. Rep. 368, 1–117 (2002).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support of AFOSR-MURI award FA9550-09-1-0617, partial support from NSF Grant PHY11-25915, and thank C. H. Greene, J. P. D’Incao and J. Wang for discussions on the method and R. Grimm for providing their original data.

Author information

Author notes

  1. Yujun Wang

    Present address: Present address: Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA.,

Authors and Affiliations

  1. Joint Quantum Institute, University of Maryland and NIST, College Park, Maryland 20742, USA

    Yujun Wang & Paul S. Julienne

Authors
  1. Yujun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul S. Julienne
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y.W. and P.S.J. both contributed equally to writing the manuscript. Y.W. planned the project in consultation with P.S.J. and implemented the numerical calculations.

Corresponding author

Correspondence to Paul S. Julienne.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Julienne, P. Universal van der Waals physics for three cold atoms near Feshbach resonances. Nature Phys 10, 768–773 (2014). https://doi.org/10.1038/nphys3071

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3071

This article is cited by

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