The European Physical Journal D

, Volume 65, Issue 1–2, pp 25–32 | Cite as

Scaling of the interaction in BECs at large scattering lengths

  • R. Sarjonen
  • M. SaarelaEmail author
  • F. Mazzanti
Regular Article Bose-Einstein condensates


We have studied the scaling of the interaction in Bose-Einstein condensates of ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We find that the effective interaction in the metastable, open channel, gaseous phase scales well with the scattering length in the range analyzed. Based on this we show that for increasing scattering lengths, or equivalently increasing densities, the system becomes less correlated, and that at large scattering lengths Bragg scattering experiments can directly measure the effective two-body potential in momentum space. This work is motivated by the recent Bragg-scattering measurements in 85Rb by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)], where the results in the line shifts show clear deviations from the simple contact interaction. We show that those results are well described by a soft spheres potential with parameters chosen to scale in scattering length units. So far the resolution in the experiments does not reveal details on the frequency dependence in the dynamic structure function S(k,ω) and we show that the Feynman spectrum determines the measured line shifts. We also construct the effective atom-atom interaction from two coupled channels, open and closed, assuming that the Feshbach resonance dominates the closed channel. The resonance energy and the scattering length a of the system are tunable by magnetic fields. We derive the T-matrix of such a system and use renormalization to calculate the bound state energy as a function of the magnetic field and make comparison with available experiments. The s-wave phase shifts determine the local, effective open-channel interaction, but if no scaling is used in the cut-off parameters of the renormalization the phase shift resembles more and more the ones obtained from the contact interaction with increasing scattering length. This leads to clear deviations from the measured line shift experiments.


Line Shift Feshbach Resonance Closed Channel Bound State Energy Soft Sphere 


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  1. 1.
    D.M. Stamper-Kum, A.P. Chikkatur, A. Gorlitz, S. Inouye, S. Gupta, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 83, 2876 (1999)ADSCrossRefGoogle Scholar
  2. 2.
    J. Steinhauer, R. Ozeri, N. Katz, N. Davidson, Phys. Rev. Lett. 88, 120407 (2002)ADSCrossRefGoogle Scholar
  3. 3.
    R. Ozeri, N. Katz, J. Steinhauer, N. Davidson, Rev. Mod. Phys. 77, 187 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    P.T. Ernst, S. Götze, J.S. Krause, K. Pyka, D.S. Lühmann, D. Pfankuche, K. Sengstock, Nature Phys. 6, 56 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    S.B. Papp, J.M. Pino, R.J. Wild, S. Rosen, C.E. Wieman, D.S. Jin, E.A. Cornell, Phys. Rev. Lett. 101, 135301 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    F. Mazzanti, A. Polls, A. Fabrocini, Phys. Rev. A 67, 063615 (2003)ADSCrossRefGoogle Scholar
  7. 7.
    S. Giorgini, J. Boronat, J. Casulleras, Phys. Rev. A 60, 5129 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    H. Feshbach, Ann. Phys. 19, 287 (1962)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    E. Feenberg, Theory of Quantum Fluids (Academic, New York, 1969)CrossRefGoogle Scholar
  10. 10.
    V. Apaja, J. Halinen, V. Halonen, E. Krotscheck, M. Saarela, Phys. Rev. B 55, 12925 (1997)ADSCrossRefGoogle Scholar
  11. 11.
    E. Krotscheck, Phys. Rev. B 33, 3158 (1986)ADSCrossRefGoogle Scholar
  12. 12.
    C.C. Chang, C.E. Campbell, Phys. Rev. B 13, 3779 (1976)ADSCrossRefGoogle Scholar
  13. 13.
    S.J.J.M.F. Kokkelmans, J.N. Milstein, M.L. Chiofalo, R. Walser, M.J. Holland, Phys. Rev. A 65, 053617 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    M. Saarela, in Introduction to Modern Methods of Quantum Many-Body Theory and Their Applications, Series on Advances in Quantum Many-Body Theory (World-Scientific, London, 2002), Vol. 7Google Scholar
  15. 15.
    A. Polls, F. Mazzanti, in Introduction to Modern Methods of Quantum Many-Body Theory and Their Applications, Series on Advances in Quantum Many-Body Theory (World-Scientific, London, 2002), Vol. 7, pp. 49–119Google Scholar
  16. 16.
    R.A. Smith, A. Kallio, M. Pouskari, P. Toropainen, Nucl. Phys. A 328, 186 (1979)ADSCrossRefGoogle Scholar
  17. 17.
    G.E. Brown, A.D. Jackson, The nucleon-nucleon interaction (North-Holland, Amsterdam, 1976)ADSCrossRefGoogle Scholar
  18. 18.
    S.J.J.M.F. Kokkelmans, M.J. Holland, Phys. Rev. Lett. 89, 180401 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    E.A. Donley, N.R. Claussen, S.T. Thompson, C.E. Wieman, Nature 417, 529 (2002)ADSCrossRefGoogle Scholar
  20. 20.
    T. Köhler, K. Góral, P.S. Julienne, Rev. Mod. Phys. 78, 1311 (2006)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of OuluOuluFinland
  2. 2.Dep. de Fisica i Enginyeria NuclearUniversitat Politecnica de CatalunyaBarcelonaSpain

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