The European Physical Journal Special Topics

, Volume 203, Issue 1, pp 87–116 | Cite as

Spin squeezing in finite temperature Bose-Einstein condensates: Scaling with the system size

  • A. SinatraEmail author
  • E. Witkowska
  • Y. Castin
Regular Article


We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number N →∞ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction ⟨N nc⟩/N in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.


European Physical Journal Special Topic Thermodynamic Limit Condensed Fraction Condensate Mode Hermitian Part 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Kitagawa, M. Ueda, Phys. Rev. A 47, 5138 (1993)ADSCrossRefGoogle Scholar
  2. 2.
    G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A.G. Mann, S. Chang, A.N. Luiten, C. Salomon, Phys. Rev. Lett. 82, 4619 (1999)ADSCrossRefGoogle Scholar
  3. 3.
    D.J. Wineland, J.J. Bollinger, W.M. Itano, D.J. Heinzen, Phys. Rev. A 50, 67 (1994)ADSCrossRefGoogle Scholar
  4. 4.
    A. Sorensen, L.M. Duan, J.I. Cirac, P. Zoller, Nature 409, 63 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    I.D. Leroux, M.H. Schleier-Smith, V. Vuletić, Phys. Rev. Lett. 104, 073602 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    C. Gross, T. Zibold, E. Nicklas, J. Estève, M.K. Oberthaler, Nature 464, 1165 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    M.F. Riedel, P. Böhi, LiYun, T.W. Hänsch, A. Sinatra, P. Treutlein, Nature 464, 1170 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    Yun Li, Y. Castin, A. Sinatra, Phys. Rev. Lett. 100, 210401 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    A. Sinatra, E. Witkowska, J.-C. Dornstetter, Yun Li, Y. Castin, Phys. Rev. Lett. (2011)Google Scholar
  10. 10.
    G. Ferrini, D. Spehner, A. Minguzzi, F.W.J. Hekking, Phys. Rev. A 84, 043628 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    A. Sinatra, J.-C. Dornstetter, Y. Castin, Frontiers of Physics 7, 86(2012), 10.1007/s11467-011-0219-7ADSCrossRefGoogle Scholar
  12. 12.
    I.D. Leroux, M.H. Schleier-Smith, Hao Zhang V., Vuletić, Phys. Rev. A 85, 013803 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    Y. Castin, J. Dalibard, Phys. Rev. A 55, 4330 (1997)ADSCrossRefGoogle Scholar
  14. 14.
    A. Sinatra, Y. Castin, Eur. Phys. J. B 4, 247 (1998)CrossRefGoogle Scholar
  15. 15.
    A.B. Kuklov, J.L. Birman, Phys. Rev. A 63, 013609 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    A. Sinatra, Y. Castin, E. Witkowska, Phys. Rev. A 75, 033616 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    A. Sinatra, Y. Castin, Phys. Rev. A 78, 053615 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    A. Sinatra, Y. Castin, E. Witkowska, Phys. Rev. A 80, 033614 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    U.V. Poulsen, K. Mølmer, Phys. Rev. A 64, 013616 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    A. Søndberg Sørensen, Phys. Rev. A 65, 043610 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    Y. Kagan, B.V. Svistunov, G.V. Shlyapnikov, Sov. Phys. JETP 75, 387 (1992)Google Scholar
  22. 22.
    K. Damle, S.N. Majumdar, S. Sachdev, Phys. Rev. A 54, 5037 (1996)ADSCrossRefGoogle Scholar
  23. 23.
    K. Goral, M. Gajda, K. Rzażewski, Optics Express 8, 92 (2001)ADSCrossRefGoogle Scholar
  24. 24.
    M.J. Davis, S.A. Morgan, K. Burnett, Phys. Rev. Lett. 87, 160402 (2001)ADSCrossRefGoogle Scholar
  25. 25.
    C. Lobo, A. Sinatra, Y. Castin, Phys. Rev. Lett. 92, 020403 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    M.J. Steel, M.K. Olsen, L.I. Plimak, P.D. Drummond, S.M. Tan, M.J. Collett, D.F. Walls, R. Graham, Phys. Rev. A 58 4824 (1998)ADSCrossRefGoogle Scholar
  27. 27.
    A. Sinatra, Y. Castin, C. Lobo, J. Mod. Opt. 47, 2629 (2000)MathSciNetADSzbMATHGoogle Scholar
  28. 28.
    A. Sinatra, C. Lobo, Y. Castin, Phys. Rev. Lett. 87, 210404 (2001)ADSCrossRefGoogle Scholar
  29. 29.
    A. Sinatra, C. Lobo, Y. Castin, J. Phys. B 35, 3599 (2002)ADSCrossRefGoogle Scholar
  30. 30.
    L. Pricoupenko, Y. Castin, J. Phys. A 40, 12863 (2007)MathSciNetADSzbMATHCrossRefGoogle Scholar
  31. 31.
    Y. Castin, R. Dum, Phys. Rev. A 57, 3008 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    M. Girardeau, R. Arnowitt, Phys. Rev. 113, 755 (1959)MathSciNetADSzbMATHCrossRefGoogle Scholar
  33. 33.
    P. Carruthers, M. Nieto, Rev. Mod. Phys. 40, 411 (1968)ADSCrossRefGoogle Scholar
  34. 34.
    C.W. Gardiner, Phys. Rev. A 56, 1414 (1997)ADSCrossRefGoogle Scholar
  35. 35.
    S. Giorgini, Phys. Rev. A 57, 2949 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Castin, in Coherent atomic matter waves, Lecture Notes of the 1999 Les Houches Summer School, edited by R. Kaiser, C. Westbrook, F. David (EDP Sciences, Springer-Verlag, 2001), p. 1Google Scholar

Copyright information

© EDP Sciences and Springer 2012

Authors and Affiliations

  1. 1.Laboratoire Kastler Brossel, École Normale Supérieure, UPMC and CNRSParisFrance
  2. 2.Institute of Physics, Polish Academy of SciencesWarszawaPoland

Personalised recommendations