Few-Body Systems

, 51:113 | Cite as

Efimov Resonances in Ultracold Quantum Gases

  • F. FerlainoEmail author
  • A. Zenesini
  • M. Berninger
  • B. Huang
  • H. -C. Nägerl
  • R. Grimm


Ultracold atomic gases have developed into prime systems for experimental studies of Efimov three-body physics and related few-body phenomena, which occur in the universal regime of resonant interactions. In the last few years, many important breakthroughs have been achieved, confirming basic predictions of universal few-body theory and deepening our understanding of such systems. We review the basic ideas along with the fast experimental developments of the field, focussing on ultracold cesium gases as a well-investigated model system. Triatomic Efimov resonances, atom-dimer Efimov resonances, and related four-body resonances are discussed as central observables. We also present some new observations of such resonances, supporting and complementing the set of available data.


Feshbach Resonance Identical Boson Trimer State Atomic Threshold Loss Resonance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Efimov V.: Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B 33, 563–564 (1970)ADSCrossRefGoogle Scholar
  2. 2.
    Kraemer T., Mark M., Waldburger P., Danzl J.G., Chin C., Engeser B., Lange A.D., Pilch K., Jaakkola A., Nägerl H.-C., Grimm R.: Evidence for Efimov quantum states in an ultracold gas of cesium atoms. Nature 440, 315–318 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    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)ADSCrossRefGoogle Scholar
  4. 4.
    Huckans J.H., Williams J.R., Hazlett E.L., Stites R.W., O’Hara K.M.: Three-body recombination in a three-state fermigas with widely tunable interactions. Phys. Rev. Lett. 102, 165302 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    Knoop S., Ferlaino F., Mark M., Berninger M., Schöbel H., Nägerl H.-C., Grimm R.: Observation of an Efimov-like trimer resonance in ultracold atom-dimer scattering. Nat. Phys. 5, 227–230 (2009)CrossRefGoogle Scholar
  6. 6.
    Zaccanti M., Deissler B., D’Errico C., Fattori M., Jona-Lasinio M., Müller S., Roati G., Inguscio M., Modugno G.: Observation of an Efimov spectrum in an atomic system. Nat. Phys. 5, 586 (2009)CrossRefGoogle Scholar
  7. 7.
    Barontini G., Weber C., Rabatti F., Catani J., Thalhammer G., Inguscio M., Minardi F.: Observation of heteronuclear atomic Efimov resonances. Phys. Rev. Lett. 103, 043201 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Gross N., Shotan Z., Kokkelmans S., Khaykovich L.: Observation of universality in ultracold 7Li three-body recombination. Phys. Rev. Lett. 103, 163202 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    Pollack S.E., Dries D., Hulet R.G.: Universality in three- and four-body bound states of ultracold atoms. Science 326, 1683–1686 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    Nakajima S., Horikoshi M., Mukaiyama T., Naidon P., Ueda M.: Nonuniversal Efimov atom-dimer resonances in a three-component mixture of 6Li. Phys. Rev. Lett. 105, 023201 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    Gross N., Shotan Z., Kokkelmans S., Khaykovich L.: Nuclear-spin-independent short-range three-body physics in ultracold atoms. Phys. Rev. Lett. 105, 103203 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    Lompe T., Ottenstein T.B., Serwane F., Viering K., Wenz A.N., Zürn, G., Jochim S., Jochim G.: Atom-dimer scattering in a three-component Fermi gas. Phys. Rev. Lett. 105, 103201 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    Nakajima S., Horikoshi M., Mukaiyama T., Naidon P., Ueda M.: Measurement of an Efimov trimer binding energy in a three-component mixture of 6Li. Phys. Rev. Lett. 106, 143201 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Efimov V.: Giant trimer true to scale. Nat. Phys. 5, 533–534 (2009)CrossRefGoogle Scholar
  15. 15.
    Greene C.H.: Universal insights from few-body land. Phys. Today 63(3), 40–45 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Ferlaino F., Grimm R.: Forty years of Efimov physics: How a bizarre prediction turned into a hot topic. Physics 3, 9 (2010)CrossRefGoogle Scholar
  17. 17.
    Efimov V.: Low-energy properties of three resonantly interacting particles. Sov. J. Nucl. Phys. 29, 546–553 (1979)Google Scholar
  18. 18.
    Ferlaino F., Knoop S., Berninger M., Harm W., D’Incao J.P., Nägerl H.-C., Grimm R.: Evidence for universal four-body states tied to an Efimov trimer. Phys. Rev. Lett. 102, 140401 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    Berninger M., Zenesini A., Huang B., Harm W., Nägerl H.-C., Ferlaino F., Grimm R., Julienne P.S., Hutson J.M.: Universality of the three-body parameter for Efimov states in ultracold cesium. Phys. Rev. Lett. 107, 120401 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    Taylor J.R.: Scattering Theory: The Quantum Theory of Nonrelativistic Collisions. Dover Books on Engineering (1983)Google Scholar
  21. 21.
    Chin C., Grimm R., Julienne P.S., Tiesinga E.: Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    Gao B.: Quantum-defect theory of atomic collisions and molecular vibration spectra. Phys. Rev. A 58, 4222–4225 (1998)ADSCrossRefGoogle Scholar
  23. 23.
    Braaten E., Hammer H.-W.: Universality in few-body systems with large scattering length. Phys. Rep. 428, 259–390 (2006)MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Derevianko A., Johnson W.R., Safronova M.S., Babb J.F.: High-precision calculations of dispersion coefficients, static dipole polarizabilities, and atom-wall interaction constants for alkali-metal atoms. Phys. Rev. Lett. 82, 3589–3592 (1999)ADSCrossRefGoogle Scholar
  25. 25.
    Jensen A.S., Riisager K., Fedorov D.V., Garrido E.: Structure and reactions of quantum halos. Rev. Mod. Phys. 76, 215–261 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    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)ADSCrossRefGoogle Scholar
  27. 27.
    Petrov D.S.: Three-boson problem near a narrow Feshbach resonance. Phys. Rev. Lett. 93, 143201 (2004)ADSCrossRefGoogle Scholar
  28. 28.
    Chin C., Vuletić V., Kerman A.J., Chu S.: High resolution Feshbach spectroscopy of cesium. Phys. Rev. Lett. 85, 2717 (2000)ADSCrossRefGoogle Scholar
  29. 29.
    Chin C., Vuletić V., Kerman A.J., Chu S., Tiesinga E., Leo P.J., Williams C.J.: Precision Feshbach spectroscopy of ultracold Cs2. Phys. Rev. A 70, 032701 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    Mark M., Ferlaino F., Knoop S., Danzl J.G., Kraemer T., Chin C., Nägerl H.-C., Grimm R.: Spectroscopy of ultracold trapped cesium Feshbach molecules. Phys. Rev. A 76, 042514 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    Berninger, M., Zenesini, A., Huang, B., Nägerl, H.-C., Ferlaino, F., Grimm, R., Julienne, P.S., Hutson, J.M.: High magnetic-field scattering properties of ultracold cs atoms (2011, In preparation)Google Scholar
  32. 32.
    Leo P.J., Williams C.J., Julienne P.S.: Collision properties of ultracold 133Cs atoms. Phys. Rev. Lett. 85, 2721–2724 (2000)ADSCrossRefGoogle Scholar
  33. 33.
    Zenesini, A., Berninger, M., Huang, B., Nägerl, H.-C., Ferlaino, F., Grimm, R.: Creation of Bose Einstein condensates of cesium at high magnetic fields (2011, In preparation)Google Scholar
  34. 34.
    Lee M.D., Köhler T., Julienne P.S.: Excited Thomas–Efimov levels in ultracold gases. Phys. Rev. A 76, 012720 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    Chin C., Vuletić V., Kerman A.J., Chu S.: High precision Feshbach spectroscopy of ultracold cesium collisions. Nucl. Phys. A 684, 641C–645C (2001)ADSCrossRefGoogle Scholar
  36. 36.
    Gustavsson M., Haller E., Mark M.J., Danzl J.G., Rojas-Kopeinig G., Nägerl H.-C.: Control of interaction-induced dephasing of Bloch oscillations. Phys. Rev. Lett. 100, 080404 (2008)ADSCrossRefGoogle Scholar
  37. 37.
    Gustavsson, M.: A quantum gas with tunable interactions in an optical lattice. PhD thesis, University of Innsbruck (2008)Google Scholar
  38. 38.
    Nielsen E., Macek J.H.: Low-energy recombination of identical bosons by three-body collisions. Phys. Rev. Lett. 83, 1566–1569 (1999)ADSCrossRefGoogle Scholar
  39. 39.
    Esry B.D., Greene C.H., Burke J.P.: Recombination of three atoms in the ultracold limit. Phys. Rev. Lett. 83, 1751–1754 (1999)ADSCrossRefGoogle Scholar
  40. 40.
    Weber T., Herbig J., Mark M., Nägerl H.-C., Grimm R.: Three-body recombination at large scattering lengths in an ultracold atomic gas. Phys. Rev. Lett. 91, 123201 (2003)ADSCrossRefGoogle Scholar
  41. 41.
    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)ADSCrossRefGoogle Scholar
  42. 42.
    Wenz A.N., Lompe T., Ottenstein T.B., Serwane F., Zürn G., Jochim S.: Universal trimer in a three-component Fermi gas. Phys. Rev. A 80, 040702(R) (2009)ADSCrossRefGoogle Scholar
  43. 43.
    D’Incao J.P., Suno H., Esry B.D.: Limits on universality in ultracold three-boson recombination. Phys. Rev. Lett. 93, 123201 (2004)ADSCrossRefGoogle Scholar
  44. 44.
    Braaten E., Hammer H.W.: Enhanced dimer relaxation in an atomic and molecular Bose-Einstein condensate. Phys. Rev. A 70, 042706 (2004)ADSCrossRefGoogle Scholar
  45. 45.
    D’Incao J.P., Esry B.D.: Scattering length scaling laws for ultracold three-body collisions. Phys. Rev. Lett. 94, 213201 (2005)ADSCrossRefGoogle Scholar
  46. 46.
    Braaten E., Hammer H.-W.: Resonant dimer relaxation in cold atoms with a large scattering length. Phys. Rev. A 75, 052710 (2007)ADSCrossRefGoogle Scholar
  47. 47.
    Weber T., Herbig J., Mark M., Nägerl H.-C., Grimm R.: Bose-Einstein condensation of cesium. Science 299, 232–235 (2003)ADSCrossRefGoogle Scholar
  48. 48.
    Kraemer T., Herbig J., Mark M., Weber T., Chin C., Nägerl H.-C., Grimm R.: Optimized production of a cesium Bose-Einstein condensate. Appl. Phys. B 79, 1013–1019 (2004)ADSCrossRefGoogle Scholar
  49. 49.
    Rychtarik D., Engeser B., Nägerl H.-C., Grimm R.: Two-dimensional Bose-Einstein condensate in an optical surface trap. Phys. Rev. Lett. 92, 173003 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    Nägerl, H.-C., Kraemer, T., Mark, M., Waldburger, P., Danzl, J.G., Chin, C., Engeser, B., Lange, A.D., Pilch, K., Jaakkola, A., Grimm, R.: Experimental evidence for Efimov quantum states. In: Atomic 20 Physics AIP Conference Proceedings, vol. 869, pp. 269–277 (2006)Google Scholar
  51. 51.
    Bringas F., Yamashita M.T., Frederico T.: Triatomic continuum resonances for large negative scattering lengths. Phys. Rev. A 69, 040702 (2004)ADSCrossRefGoogle Scholar
  52. 52.
    Yamashita M., Frederico T., Tomio L.: Three-boson recombination at ultralow temperatures. Phys. Lett. A 363, 468–472 (2007)ADSCrossRefGoogle Scholar
  53. 53.
    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: At. Mol. Opt. Phys. 42, 044016 (2009)ADSCrossRefGoogle Scholar
  54. 54.
    Platter L., Shepard J.R.: Scaling functions applied to three-body recombination of 133Cs atoms. Phys. Rev. A 78, 062717 (2008)ADSCrossRefGoogle Scholar
  55. 55.
    Massignan P., Stoof H.T.C.: Efimov states near a Feshbach resonance. Phys. Rev. A 78, 030701 (2008)ADSCrossRefGoogle Scholar
  56. 56.
    Jona-Lasinio M., Pricoupenko L.: Three resonant ultracold bosons: Off-resonance effects. Phys. Rev. Lett. 104, 023201 (2010)ADSCrossRefGoogle Scholar
  57. 57.
    Ferlaino F., Knoop S., Grimm R.: Cold molecules: theory, experiment, applications. In: Krems, R.V., Friedrich, B., Stwalley, W.C. (eds) Ultracold Feshbach molecules, CRC Press, Boca Raton (2009)Google Scholar
  58. 58.
    Knoop, S., Ferlaino, F., Berninger, M., Mark, M., Nägerl, H.-C., Grimm, R.: Observation of an Efimov resonance in an ultracold mixture of atoms and weakly bound dimers. J. Phys.: Conf. Ser 194, 012064, arXiv:0907.4510 (2009)Google Scholar
  59. 59.
    Braaten E., Hammer H.-W.: Erratum: Resonant dimer relaxation in cold atoms with a large scattering length. Phys. Rev. A 79, 039905 (2009)ADSCrossRefGoogle Scholar
  60. 60.
    Helfrich K., Hammer H.W.: Resonant atom-dimer relaxation in ultracold atoms. Europhys. Lett. 86, 53003 (2009)ADSCrossRefGoogle Scholar
  61. 61.
    Thomas L.H.: The interaction between a neutron and a proton and the structure of H3. Phys. Rev. 47, 903–909 (1935)ADSzbMATHCrossRefGoogle Scholar
  62. 62.
    Bedaque P.F., Hammer H.-W., van Kolck U.: Renormalization of the three-body system with short-range interactions. Phys. Rev. Lett. 82, 463–467 (1999)ADSCrossRefGoogle Scholar
  63. 63.
    Soldán P., Cvitaš M.T., Hutson J.M.: Three-body nonadditive forces between spin-polarized alkali-metal atoms. Phys. Rev. A 67, 054702 (2003)ADSCrossRefGoogle Scholar
  64. 64.
    Naidon P., Ueda M.: The Efimov effect in lithium 6. C.R. Physique 12, 13 (2011)ADSCrossRefGoogle Scholar
  65. 65.
    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)ADSCrossRefGoogle Scholar
  66. 66.
    Pricoupenko L.: Crossover in the Efimov spectrum. Phys. Rev. A 82, 043633 (2010)ADSCrossRefGoogle Scholar
  67. 67.
    Wang Y., D’Incao J.P., Esry B.D.: Ultracold three-body collisions near Feshbach resonances. Phys. Rev. A 83, 042710 (2011)ADSCrossRefGoogle Scholar
  68. 68.
    Thøgersen M., Fedorov D.V., Jensen A.S.: Universal properties of Efimov physics beyond the scattering length. Phys. Rev. A 78, 020501(R) (2008)ADSCrossRefGoogle Scholar
  69. 69.
    Ji, C., Phillips, D.R., Platter, L.: The three-boson system at next-to-leading order in the pionless EFT. arXiv:1106.3837, (2011)Google Scholar
  70. 70.
    Williams J.R., Hazlett E.L., Huckans J.H., Stites R.W., Zhang Y., O’Hara K.M.: Evidence for an excited-state Efimov trimer in a three-component fermigas. Phys. Rev. Lett. 103, 130404 (2009)ADSCrossRefGoogle Scholar
  71. 71.
    Amado R.D., Greenwood F.C.: There is no Efimov effect for four or more particles. Phys. Rev. D 7, 2517 (1973)MathSciNetADSCrossRefGoogle Scholar
  72. 72.
    Adhikari S.K., Fonseca A.C.: Four-body Efimov effect in a Born-Oppenheimer model. Phys. Rev. D 24, 416–425 (1981)ADSCrossRefGoogle Scholar
  73. 73.
    Naus H.W.L., Tjon J.A.: The Efimov effect in a four-body system. Few-Body Syst. 2, 121–126 (1987)ADSCrossRefGoogle Scholar
  74. 74.
    Sørensen O., Fedorov D.V., Jensen A.S.: Correlated trapped bosons and the many-body Efimov effect. Phys. Rev. Lett. 89, 173002 (2002)ADSCrossRefGoogle Scholar
  75. 75.
    Platter L., Hammer H.-W., Meißner U.-G.: Four-boson system with short-range interactions. Phys. Rev. A 70, 052101 (2004)ADSCrossRefGoogle Scholar
  76. 76.
    Yamashita M.T., Tomio L., Delfino A., Frederico T.: Four-boson scale near a Feshbach resonance. Europhys. Lett. 75, 555–561 (2006)ADSCrossRefGoogle Scholar
  77. 77.
    Hanna G.J., Blume D.: Energetics and structural properties of three-dimensional bosonic clusters near threshold. Phys. Rev. A 74, 063604 (2006)ADSCrossRefGoogle Scholar
  78. 78.
    Thøgersen M., Fedorov D.V., Jensen A.S.: N-body Efimov states of trapped bosons. Europhys. Lett. 83, 30012 (2008)ADSCrossRefGoogle Scholar
  79. 79.
    Castin Y., Mora C., Pricoupenko L.: Four-body Efimov effect for three fermions and a lighter particle. Phys. Rev. Lett. 105, 223201 (2010)ADSCrossRefGoogle Scholar
  80. 80.
    Hammer H.-W., Platter L.: Universal properties of the four-body system with large scattering length. Eur. Phys. J. A 32, 113–120 (2007)ADSCrossRefGoogle Scholar
  81. 81.
    von Stecher J., D’Incao J.P., Greene C.H.: Signatures of universal four-body phenomena and their relation to the Efimov effect. Nat. Phys. 5, 417–421 (2009)CrossRefGoogle Scholar
  82. 82.
    D’Incao J.P., von Stecher J., Greene C.H.: Universal four-boson states in ultracold molecular gases: Resonant effects in dimer–dimer collisions. Phys. Rev. Lett. 103, 033004 (2009)ADSCrossRefGoogle Scholar
  83. 83.
    Mehta N.P., Rittenhouse S.T., D’Incao J.P., von Stecher J., Greene C.H.: General theoretical description of n-body recombination. Phys. Rev. Lett. 103, 153201 (2009)ADSCrossRefGoogle Scholar
  84. 84.
    von Stecher J.: Weakly bound cluster states of Efimov character. J. Phys. B: At. Mol. Opt. Phys. 43, 101002 (2010)ADSCrossRefGoogle Scholar
  85. 85.
    von Stecher, J.: Universal five- and six-body droplets tied to an Efimov trimer. arXiv:1106.2319 (2011)Google Scholar
  86. 86.
    Bartenstein M., Altmeyer A., Riedl S., Geursen R., Jochim S., Chin C., Hecker Denschlag J., Grimm R., Simoni A., Tiesinga E., Williams C.J., Julienne P.S.: Precise determination of 6Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules. Phys. Rev. Lett. 94, 103201 (2005)ADSCrossRefGoogle Scholar
  87. 87.
    Lompe T., Ottenstein T.B., Servane F., Wenz A.N., Zürn G., Jochim S.: Radio-frequency association of Efimov trimers. Science 330, 940 (2010)ADSCrossRefGoogle Scholar
  88. 88.
    D’Incao J.P., Esry B.D.: Enhancing the observability of the Efimov effect in ultracold atomic gas mixtures. Phys. Rev. A 73, 030703(R) (2006)Google Scholar
  89. 89.
    D’Incao J.P., Esry B.D.: Mass dependence of ultracold three-body collision rates. Phys. Rev. A 73, 030702 (2006)CrossRefGoogle Scholar
  90. 90.
    Nishida Y., Tan S.: Universal fermigases in mixed dimensions. Phys. Rev. Lett. 101, 170401 (2008)MathSciNetADSCrossRefGoogle Scholar
  91. 91.
    Nishida Y., Tan S.: Confinement-induced Efimov resonances in Fermi–Fermi mixtures. Phys. Rev. A 79, 060701(R) (2009)ADSGoogle Scholar
  92. 92.
    Levinsen J., Tiecke T.G., Walraven J.T.M., Petrov D.S.: Atom-dimer scattering and long-lived trimers in fermionic mixtures. Phys. Rev. Lett 103, 153202 (2009)ADSCrossRefGoogle Scholar
  93. 93.
    Wang Y., D’Incao J.P., Greene C.H.: Efimov effect for three interacting bosonic dipoles. Phys. Rev. Lett. 106, 233201 (2011)ADSCrossRefGoogle Scholar
  94. 94.
    Petrov D.S., Salomon C., Shlyapnikov G.V.: Weakly bound molecules of fermionic atoms. Phys. Rev. Lett. 93, 090404 (2004)ADSCrossRefGoogle Scholar
  95. 95.
    von Stecher J., Greene C.H.: Spectrum and dynamics of the BCS-BEC crossover from a few-body perspective. Phys. Rev. Lett. 99, 090402 (2007)CrossRefGoogle Scholar
  96. 96.
    Liu X.-J., Hu H., Drummond P.D.: Virial expansion for a strongly correlated fermigas. Phys. Rev. Lett. 102, 160401 (2009)ADSCrossRefGoogle Scholar
  97. 97.
    Tan S.: Energetics of a strongly correlated Fermi gas. Ann. Phys. 323, 2952–2970 (2008)ADSzbMATHCrossRefGoogle Scholar
  98. 98.
    Braaten E.: How the tail wags the dog in ultracold atomic gases. Physics 2, 9 (2009)CrossRefGoogle Scholar
  99. 99.
    Daley A.J., Taylor J.M., Diehl S., Baranov M., Zoller P.: Atomic three-body loss as a dynamical three-body interaction. Phys. Rev. Lett. 102, 040402 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • F. Ferlaino
    • 1
    Email author
  • A. Zenesini
    • 1
  • M. Berninger
    • 1
  • B. Huang
    • 1
  • H. -C. Nägerl
    • 1
  • R. Grimm
    • 1
    • 2
  1. 1.Institut für Experimentalphysik and Zentrum für QuantenphysikUniversität InnsbruckInnsbruckAustria
  2. 2.Institut für Quantenoptik und QuanteninformationÖsterreichische Akademie der WissenschaftenInnsbruckAustria

Personalised recommendations