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Few-Body Physics in a Many-Body World

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Abstract

The study of quantum mechanical few-body systems is a century old pursuit relevant to countless subfields of physics. While the two-body problem is generally considered to be well-understood theoretically and numerically, venturing to three or more bodies brings about complications but also a host of interesting phenomena. In recent years, the cooling and trapping of atoms and molecules has shown great promise to provide a highly controllable environment to study few-body physics. However, as is true for many systems where few-body effects play an important role the few-body states are not isolated from their many-body environment. An interesting question then becomes if or (more precisely) when we should consider few-body states as effectively isolated and when we have to take the coupling to the environment into account. Using some simple, yet non-trivial, examples I will try to suggest possible approaches to this line of research.

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References

  1. Simon B.: The bound state of weakly coupled Schrödinger operators in one and two dimensions. Ann. Phys. 97, 288–297 (1976)

    Article  ADS  Google Scholar 

  2. Volosniev A.G., Fedorov D.V., Jensen A.S., Zinner N.T.: Model independence in two dimensions and polarized cold dipolar molecules. Phys. Rev. Lett. 106, 250401 (2011)

    Article  ADS  Google Scholar 

  3. 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 

  4. Bruch L.W., Tjon J.A.: Binding of three identical bosons in two dimensions. Phys. Rev. A. 19, 425–432 (1979)

    Article  ADS  Google Scholar 

  5. Nielsen E., Fedorov D.V., Jensen A.S.: Three-body halos in two dimensions. Phys. Rev. A. 56, 3287–3290 (1997)

    Article  ADS  Google Scholar 

  6. Nielsen E., Fedorov D.V., Jensen A.S., Garrido E.: Three-body halos in two dimensions. Phys. Rep. 347, 373–459 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Nishida Y., Tan S.: Liberating Efimov physics from three dimensions. Few Body Syst. 51, 191–206 (2011)

    Article  ADS  Google Scholar 

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

    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. Davis K.B. et al.: Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995)

    Article  ADS  Google Scholar 

  11. Anderson M.H. et al.: Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995)

    Article  ADS  Google Scholar 

  12. Bradley C.C. et al.: Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions. Phys. Rev. Lett. 75, 1687–1690 (1995)

    Article  ADS  Google Scholar 

  13. Inouye S. et al.: Observation of Feshbach resonances in a Bose-Einstein condensate. Nature 392, 151–154 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Giorgini S., Pitaevskii L.P., Stringari S.: Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  17. Sørensen P.K. et al.: Three-body recombination at finite energy within an optical model. Phys. Rev. A. 88, 042518 (2013)

    Article  ADS  Google Scholar 

  18. Nishida Y.: Casimir interaction among heavy fermions in the BCS-BEC crossover. Phys. Rev. A. 79, 013629 (2009)

    Article  ADS  Google Scholar 

  19. MacNeill D., Zhou F.: Pauli blocking effect on Efimov states near Feshbach resonance. Phys. Rev. Lett. 106, 145301 (2011)

    Article  ADS  Google Scholar 

  20. Endo, S., Ueda, M.: Perfect screening of the inter-polaronic interaction. Preprint arXiv:1309.7797 (2013)

    Google Scholar 

  21. Nygaard, N.G., Zinner, N.T.: The fate of the Efimov effect in a many-body world. Preprint arXiv:1110.5854 (2011)

    Google Scholar 

  22. Skornyakov G.V., Ter-Martirosian K.A.: Three-body problem with short-range forces. Neutron scattering of deutrons at small energy. Zh. Eksp. Teor. Fiz. 31, 775 (1956)

    Google Scholar 

  23. Pricoupenko L.: Crossover in the Efimov spectrum. Phys. Rev. A. 82, 043633 (2011)

    Article  ADS  Google Scholar 

  24. Huckans J.H. et al.: Three-body recombination in a three-state Fermi gas with widely tunable interactions. Phys. Rev. Lett. 102, 165302 (2009)

    Article  ADS  Google Scholar 

  25. Lompe T. et al.: Radio-frequency association of Efimov trimers. Science 330, 940–944 (2010)

    Article  ADS  Google Scholar 

  26. Nakajima S. et al.: Measurement of an Efimov trimer binding energy in a three-component mixture of 6Li. Phys. Rev. Lett. 106, 143201 (2011)

    Article  ADS  Google Scholar 

  27. Borzov D. et al.: Nature of 3D Bose gases near resonance. Phys. Rev. A. 85, 023620 (2012)

    Article  ADS  Google Scholar 

  28. Zhou F., Mashayekhi M.S.: Bose gases near resonance: renormalized interactions in a condensate. Ann. Phys. 328, 83–102 (2012)

    Article  ADS  Google Scholar 

  29. Jian, S.-J., Liu, W.-M., Semenoff, G.W., Zhou, F.: Universal bose gases near resonance: a rigorous solution. Preprint arXiv:1307.4263 (2013)

    Google Scholar 

  30. Zinner N.T.: Efimov states of heavy impurities in a Bose-Einstein condensate. Euro. Phys. Lett. 101, 60009 (2013)

    Article  ADS  Google Scholar 

  31. Chin, C.: Universal scaling of Efimov resonance positions in cold atom systems. Prepring arXiv:1111.1484 (2011)

    Google Scholar 

  32. Naidon P., Hiyama E., Ueda M.: Universality and the three-body parameter of helium-4 trimers. Phys. Rev. A. 86, 012502 (2012)

    Article  ADS  Google Scholar 

  33. 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 

  34. Sørensen P.K., Fedorov D.V., Jensen A.S., 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 

  35. Schmidt R., Rath S.P., Zwerger W.: Efimov physics beyond universality. Eur. Phys. J. B. 85, 386 (2012)

    Article  ADS  Google Scholar 

  36. Borbely J.S., van Rooij R., Knoop S., Vassen W.: Magnetic-field-dependent trap loss of ultracold metastable helium. Phys. Rev. A. 85, 022706 (2012)

    Article  ADS  Google Scholar 

  37. Knoop S., Borbely J.S., Vassen W., Kokkelmans S.J.J.M.F.: Universal three-body parameter in ultracold 4He*. Phys. Rev. A. 86, 062705 (2012)

    Article  ADS  Google Scholar 

  38. Combescot R., Giraud S.: Normal state of highly polarized Fermi gases: full many-body treatment. Phys. Rev. Lett. 101, 050404 (2008)

    Article  ADS  Google Scholar 

  39. Pikovski A. et al.: Interlayer superfluidity in bilayer systems of Fermionic polar molecules. Phys. Rev. Lett. 105, 215302 (2010)

    Article  ADS  Google Scholar 

  40. Baranov  M.A. et al.: Bilayer superfluidity of fermionic polar molecules: many-body effects. Phys. Rev. A. 83, 043602 (2011)

    Article  ADS  Google Scholar 

  41. Zinner N.T. et al.: Dimers, effective interactions, and pauli blocking effects in a bilayer of cold Fermionic polar molecules. Few Body Syst. 53, 369–385 (2012)

    Article  ADS  Google Scholar 

  42. Volosniev A.G. et al.: Bound states of dipolar Bosons in one-dimensional systems. New J. Phys. 15, 043046 (2013)

    Article  ADS  Google Scholar 

  43. Armstrong J.R. et al.: Layers of cold dipolar molecules in the harmonic approximation. Eur. Phys. J. D. 66, 85 (2012)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000, Aarhus C, Denmark

    Nikolaj Thomas Zinner

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  1. Nikolaj Thomas Zinner
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Correspondence to Nikolaj Thomas Zinner.

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The work of the author reported here was supported by the Sapere Aude program under the Danish Council for Independent Research.

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Zinner, N.T. Few-Body Physics in a Many-Body World. Few-Body Syst 55, 599–604 (2014). https://doi.org/10.1007/s00601-014-0802-x

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