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Efimov Physics from the Functional Renormalization Group

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Abstract

Few-body physics related to the Efimov effect is discussed using the functional renormalization group method. After a short review of renormalization in its modern formulation we apply this formalism to the description of scattering and bound states in few-body systems of identical bosons and distinguishable fermions with two and three components. The Efimov effect leads to a limit cycle in the renormalization group flow. Recently measured three-body loss rates in an ultracold Fermi gas of 6Li atoms are explained within this framework. We also discuss briefly the relation to the many-body physics of the BCS–BEC crossover for two-component fermions and the formation of a trion phase for the case of three species.

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References

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  3. Efimov V.: Energy levels of three resonantly-interacting particles. Nucl. Phys. A 210, 157 (1973)

    Article  ADS  Google Scholar 

  4. Bedaque P.F., Hammer H.W., van Kolck U.: Renormalization of the three-body system with short-range interactions. Phys. Rev. Lett. 82, 463 (1999)

    Article  ADS  Google Scholar 

  5. Ferlaino F., Grimm R.: Forty years of Efimov physics: How a bizarre prediction turned into a hot topic. Physics 3, 9 (2010)

    Article  Google Scholar 

  6. 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 

  7. 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 

  8. Berges J., Tetradis N., Wetterich C.: Non-perturbative renormalization flow in quantum field theory and statistical physics. Phys. Rep. 363, 223 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Morris T.R.: Elements of the continuous renormalization group. Prog. Theor. Phys. Suppl. 131, 395 (1998)

    Article  ADS  Google Scholar 

  10. Aoki K.: Introduction to the non-perturbative renormalization group and its recent applications. Int. J. Mod. Phys. B 14, 1249 (2000)

    ADS  MATH  Google Scholar 

  11. Bagnuls C., Bervillier C.: Exact renormalization group equations: an introductory review. Phys. Rep. 348, 91 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Polonyi J.: Lectures on the functional renormalization group method. Central Eur. J. Phys. 1, 1 (2003)

    Article  ADS  Google Scholar 

  13. Salmhofer M., Honerkamp C.: Fermionic renormalization group flows—technique and theory. Prog. Theor. Phys. 105, 1 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Delamotte, B.: An introduction to the nonperturbative renormalization group. cond-mat/0702365

  15. Schaefer B.J., Wambach J.: Renormalization group approach towards the QCD phase diagram. Phys. Part. Nucl. 39, 1025 (2008)

    Article  Google Scholar 

  16. Pawlowski J.M.: Aspects of the functional renormalisation group. Ann. Phys. 322, 2831 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Rosten, O.J.: Fundamentals of the Exact Renormalization Group. arXiv:1003.1366

  18. Wetterich C.: Exact evolution equation for the effective potential. Phys. Lett. B 301, 90 (1993)

    Article  ADS  Google Scholar 

  19. Diehl S., Wetterich C.: Functional integral for ultracold fermionic atoms. Nucl. Phys. B 770, 206 (2007)

    Article  ADS  MATH  Google Scholar 

  20. Diehl S., Wetterich C.: Universality in phase transitions for ultracold fermionic atoms. Phys. Rev. A 73, 033615 (2006)

    Article  ADS  Google Scholar 

  21. Diehl, S.: Universality in the BCS-BEC crossover in cold Fermion gases. cond-mat/0701157

  22. Diehl S., Krahl H.C., Scherer M.: Three-body scattering from nonperturbative flow equations. Phys. Rev. C 78, 034001 (2008)

    Article  ADS  Google Scholar 

  23. Moroz S., Floerchinger S., Schmidt R., Wetterich C.: Efimov effect from functional renormalization. Phys. Rev. A 79, 042705 (2009)

    Article  ADS  Google Scholar 

  24. Diehl S., Floerchinger S., Gies H., Pawlowski J.M., Wetterich C.: Functional renormalization group approach to the BCS-BEC crossover. Ann. Phys. (Berlin) 522, 615 (2010)

    ADS  Google Scholar 

  25. Floerchinger, S.: Functional renormalization and ultracold quantum gases. Doctoral thesis, Universität Heidelberg (2009)

  26. Gies H., Wetterich C.: Renormalization flow of bound states. Phys. Rev. D 65, 065001 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  27. Gies H., Wetterich C.: Renormalization flow from UV to IR degrees of freedom. Acta Phys. Slov. 52, 215 (2002)

    Google Scholar 

  28. Floerchinger S., Wetterich C.: Exact flow equation for composite operators. Phys. Lett. B 680, 371 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  29. Floerchinger S.: Exact flow equation for bound states. Eur. Phys. J. C 69, 119 (2010)

    Article  ADS  Google Scholar 

  30. Birse M.C.: Functional renormalization group for two-body scattering. Phys. Rev. C 77, 047001 (2008)

    Article  ADS  Google Scholar 

  31. Skorniakov G.V., Ter-Martirosian K.A.: Three body problem for short range forces 1. Scattering of low energy neutrons by deuterons. Zh. Eksp. Teor. Phys. 31, 775 (1956)

    Google Scholar 

  32. Skorniakov G.V., Ter-Martirosian K.A.: Sov. Phys. JETP 4, 648 (1957)

    MathSciNet  Google Scholar 

  33. Bloch I., Dalibard J., Zwerger W.: Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885 (2008)

    Article  ADS  Google Scholar 

  34. Giorgini S., Pitaevskii L.P., Stringari S.: Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215 (2008)

    Article  ADS  Google Scholar 

  35. Birse M.C., Krippa B., McGovern J.A., Walet N.R.: Pairing in many-fermion systems: an exact renormalisation group treatment. Phys. Lett. B 605, 287 (2005)

    Article  ADS  Google Scholar 

  36. Diehl S., Gies H., Pawlowski J.M., Wetterich C.: Flow equations for the BCS-BEC crossover. Phys. Rev. A 76, 021602(R) (2007)

    ADS  Google Scholar 

  37. Diehl S., Gies H., Pawlowski J.M., Wetterich C.: Renormalization flow and universality for ultracold fermionic atoms. Phys. Rev. A 76, 53627 (2007)

    Article  ADS  Google Scholar 

  38. Floerchinger S., Scherer M., Diehl S., Wetterich C.: Particle-hole fluctuations in BCS-BEC crossover. Phys. Rev. B 78, 174528 (2008)

    Article  ADS  Google Scholar 

  39. Bartosch L., Kopietz P., Ferraz A.: Renormalization of the BCS-BEC crossover by order-parameter fluctuations. Phys. Rev. B 80, 104514 (2009)

    Article  ADS  Google Scholar 

  40. Floerchinger S., Scherer M.M., Wetterich C.: Modified Fermi sphere, pairing gap, and critical temperature for the BCS-BEC crossover. Phys. Rev. A 81, 063619 (2010)

    Article  ADS  Google Scholar 

  41. Petrov D.S., Salomon C., Shlyapnikov G.V.: Weakly bound dimers of fermionic atoms. Phys. Rev. Lett. 93, 090404 (2004)

    Article  ADS  Google Scholar 

  42. Krippa B., Walet N.R., Birse M.C.: Renormalization group, dimer-dimer scattering, and three-body forces. Phys. Rev. A 81, 043628 (2010)

    Article  ADS  Google Scholar 

  43. Birse, M.C., Krippa, B., Walet, N.R.: Convergence of a renormalization group approach to dimer-dimer scattering. arXiv:1011.5852

  44. Scherer, M.M., Floerchinger, S., Gies, H.: Functional renormalization for the BCS-BEC crossover. arXiv:1010.2890

  45. Floerchinger S., Schmidt R., Moroz S., Wetterich C.: Functional renormalization for trion formation in ultracold fermion gases. Phys. Rev. A 79, 013603 (2009)

    Article  ADS  Google Scholar 

  46. Kokkelmans S.J.J.M.F., Milstein J.N., Chiofalo M.L., Walser R., Holland M.J.: Resonance superfluidity: renormalization of resonance scattering theory. Phys. Rev. A 65, 053617 (2002)

    Article  ADS  Google Scholar 

  47. 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)

    Article  ADS  Google Scholar 

  48. Schmidt R., Moroz S.: Renormalization-group study of the four-body problem. Phys. Rev. A 81, 052709 (2010)

    Article  ADS  Google Scholar 

  49. Rapp A., Zarand G., Honerkamp C., Hofstetter W.: Color superfluidity and “Baryon” formation in ultracold fermions. Phys. Rev. Lett. 98, 160405 (2007)

    Article  ADS  Google Scholar 

  50. Rapp A., Hofstetter W., Zarand G.: Trionic phase of ultracold fermions in an optical lattice: a variational study. Phys. Rev. B 77, 144520 (2008)

    Article  ADS  Google Scholar 

  51. Wilczek F.: Quantum chromodynamics: lifestyles of the small and simple. Nat. Phys. 3, 375 (2007)

    Article  Google Scholar 

  52. Floerchinger S., Schmidt R., Wetterich C.: Three-body loss in lithium from functional renormalization. Phys. Rev. A 79, 053633 (2009)

    Article  ADS  Google Scholar 

  53. Braaten E., Hammer H.W., Kang D., Platter L.: Three-body recombination of 6Li atoms with large negative scattering lengths. Phys. Rev. Lett. 103, 073202 (2009)

    Article  ADS  Google Scholar 

  54. Naidon P., Ueda M.: Possible Efimov trimer state in a three-hyperfine-component Lithium-6 mixture. Phys. Rev. Lett. 103, 073203 (2009)

    Article  ADS  Google Scholar 

  55. 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)

    Article  ADS  Google Scholar 

  56. Hammer H.W., Kang D., Platter L.: Efimov physics in atom-dimer scattering of 6Li atoms. Phys. Rev. A 82, 022715 (2010)

    Article  ADS  Google Scholar 

  57. Naidon, P., Ueda, M.: The Efimov effect in lithium 6. arXiv:1008.2260v2 (2010)

  58. 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 Fermi gas. Phys. Rev. Lett. 103, 130404 (2009)

    Article  ADS  Google Scholar 

  59. Lompe T., Ottenstein T.B., Serwane F., Viering K., Wenz A.N., Zürn G., Jochim S.: Atom-dimer scattering in a three-component Fermi gas. Phys. Rev. Lett. 105, 103201 (2010)

    Article  ADS  Google Scholar 

  60. Lompe T., Ottenstein T.B., Serwane F., Wenz A.N., Zürn G., Jochim S.: Radio-frequency association of Efimov trimers. Science 330, 940 (2010)

    Article  ADS  Google Scholar 

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  1. Stefan Floerchinger

    Present address: Physics Department, Theory Unit, CERN, 1211, Geneva 23, Switzerland

Authors and Affiliations

  1. Institut für Theoretische Physik, Philosophenweg 16, 69120, Heidelberg, Germany

    Stefan Floerchinger & Sergej Moroz

  2. Physik Department, Technische Universität München, James-Franck-Straße, 85748, Garching, Germany

    Richard Schmidt

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  1. Stefan Floerchinger
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  2. Sergej Moroz
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  3. Richard Schmidt
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Correspondence to Stefan Floerchinger.

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Floerchinger, S., Moroz, S. & Schmidt, R. Efimov Physics from the Functional Renormalization Group. Few-Body Syst 51, 153–180 (2011). https://doi.org/10.1007/s00601-011-0231-z

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