Advertisement

Efimov physics beyond universality

Regular Article

Abstract

We provide an exact solution of the Efimov spectrum in ultracold gases within the standard two-channel model for Feshbach resonances. It is shown that the finite range in the Feshbach coupling makes the introduction of an adjustable three-body parameter obsolete. The solution explains the empirical relation between the scattering length a where the first Efimov state appears at the atom threshold and the van der Waals length l vdw for open-channel dominated resonances. There is a continuous crossover to the closed-channel dominated limit, where the scale in the energy level diagram as a function of the inverse scattering length 1 / a is set by the intrinsic length r associated with the Feshbach coupling. Our results provide a number of predictions for the deviations from universal scaling relations between energies and scattering lengths that can be tested in future experiments.

Keywords

Solid State and Materials 

References

  1. 1.
    C.K. Hong, Z.Y. Ou, L. Mandel, Phys. Rev. Lett. 59, 2044 (1987)ADSCrossRefGoogle Scholar
  2. 2.
    V. Efimov, Phys. Lett. B 33, 563 (1970)ADSCrossRefGoogle Scholar
  3. 3.
    V. Efimov, Nucl. Phys. A 210, 157 (1973)ADSCrossRefGoogle Scholar
  4. 4.
    T. Kraemer, M. Mark, P. Waldburger, J.G. Danzl, C. Chin, B. Engeser, A.D. Lange, K. Pilch, A. Jaakkola, H.-C. Nägerl, R. Grimm, Nature 440, 315 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    C. Chin, R. Grimm, P.S. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).ADSCrossRefGoogle Scholar
  6. 6.
    P.F. Bedaque, H.-W. Hammer, U. van Kolck, Phys. Rev. Lett. 82, 463 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    P.F. Bedaque, H.-W. Hammer, U. van Kolck, Nucl. Phys. A 646, 444 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    E. Braaten, H.-W. Hammer, Phys. Rep. 428, 259 (2006)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    J.P. D’Incao, C.H. Greene, B.D. Esry, J. Phys. B 42, 044016 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    T.B. Ottenstein, T. Lompe, M. Kohnen, A.N. Wenz, S. Jochim, Phys. Rev. Lett. 101, 203202 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    J.H. Huckans, J.R. Williams, E.L. Hazlett, R.W. Stites, K.M. O’Hara, Phys. Rev. Lett. 102, 165302 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    S.E. Pollack, D. Dries, R.G. Hulet, Science 326, 1683 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    M. Zaccanti, B. Deissler, C. D’Errico, M. Fattori, M. Jona-Lasinio, S. Müller, G. Roati, M. Inguscio, G. Modugno, Nat. Phys. 5, 586 (2009)CrossRefGoogle Scholar
  14. 14.
    N. Gross, Z. Shotan, S. Kokkelmans, L. Khaykovich, Phys. Rev. Lett. 103, 163202 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    N. Gross, Z. Shotan, S. Kokkelmans, L. Khaykovich, Phys. Rev. Lett. 105, 103203 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    M. Berninger, A. Zenesini, B. Huang, W. Harm, H.-C. Nägerl, F. Ferlaino, R. Grimm, P.S. Julienne, J.M. Hutson, Phys. Rev. Lett. 107, 120401 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    R.J. Wild, P. Makotyn, J.M. Pino, E.A. Cornell, D.S. Jin, Phys. Rev. Lett. 108, 145305 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    V.V. Flambaum, G.F. Gribakin, C. Harabati, Phys. Rev. A 59, 1998 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    C. Chin, arXiv:1111.1484v2 [cond-mat.quant-gas] (2011)Google Scholar
  20. 20.
    J. Wang, J.P. D’Incao, B.D. Esry, C.H. Greene, Phys. Rev. Lett. 108, 263001 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    D.S. Petrov, Phys. Rev. Lett. 93, 143201 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    A.O. Gogolin, C. Mora, R. Egger, Phys. Rev. Lett. 100, 140404 (2008)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    A.N. Wenz, T. Lompe, T.B. Ottenstein, F. Serwane, G. Zürn, S. Jochim, Phys. Rev. A 80, 040702(R) (2009)ADSCrossRefGoogle Scholar
  24. 24.
    J.R. Williams, E.L. Hazlett, J.H. Huckans, R.W. Stites, Y. Zhang, K.M. O’Hara, Phys. Rev. Lett. 103, 130404 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    M.H. Szymańska, K. Góral, T. Köhler, K. Burnett, Phys. Rev. A 72, 013610 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    P. Massignan, H.T.C. Stoof, Phys. Rev. A 78, 030701(R) (2008)ADSGoogle Scholar
  27. 27.
    F. Werner, L. Tarruell, Y. Castin, Eur. Phys. J. B 68, 401 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    L. Pricoupenko, Phys. Rev. A 82, 043633 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    M. Jona-Lasinio, L. Pricoupenko, Phys. Rev. Lett. 104, 023201 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    L. Pricoupenko, M. Jona-Lasinio, Phys. Rev. A 84, 062712 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    K. Góral, T. Köhler, S.A. Gardiner, E. Tiesinga, P.S. Julienne, J. Phys. B 37, 3457 (2004)ADSCrossRefGoogle Scholar
  33. 33.
    G.F. Gribakin, V.V. Flambaum, Phys. Rev. A 48, 546 (1993)ADSCrossRefGoogle Scholar
  34. 34.
    C. Wetterich, Phys. Lett. B 301, 90 (1993)ADSCrossRefGoogle Scholar
  35. 35.
    S. Diehl, H.C. Krahl, M. Scherer, Phys. Rev. C 78, 034001 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    S. Moroz, S. Floerchinger, R. Schmidt, C. Wetterich, Phys. Rev. A 79, 042705 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    G.V. Skornyakov, K.A. Ter-Martirosian, Zh. Eksp. Teor. Phys. 31, 775 (1956), [Sov. Phys. JETP 4, 648 (1957)]Google Scholar
  38. 38.
    J.V. Stecher, J.P. D’Incao, C.H. Greene, Nat. Phys. 5, 417 (2009)CrossRefGoogle Scholar
  39. 39.
    R. Schmidt, S. Moroz, Phys. Rev. A 81, 052709 (2010)ADSCrossRefGoogle Scholar
  40. 40.
    J.V. Stecher, J. Phys. B 43, 101002 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    R. Seiringer, arXiv:1204.0435v2 [math-ph] (2012)Google Scholar
  42. 42.
    C. Ji, D.R. Phillips, L. Platter, Eur. Phys. Lett. 92, 12003 (2010)CrossRefGoogle Scholar
  43. 43.
    B.M. Axilrod, E. Teller, J. Chem. Phys. 11, 299 (1943)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Physik DepartmentTechnische Universität MünchenGarchingGermany

Personalised recommendations