The European Physical Journal D

, Volume 65, Issue 1–2, pp 43–47

Integrability breakdown in longitudinaly trapped, one-dimensional bosonic gases

Regular Article Bose-Einstein condensates

Abstract

A system of identical bosons with short-range (contact) interactions is studied. Their motion is confined to one dimension by a tight lateral trapping potential and, additionally, subject to a weak harmonic confinement in the longitudinal direction. Finite delay time associated with penetration of quantum particles through each other in the course of a pairwise one-dimensional collision in the presence of the longitudinal potential makes the system non-integrable and, hence, provides a mechanism for relaxation to thermal equilibrium. To analyse this effect quantitatively in the limit of a non-degenerate gas, we develop a system of kinetic equations and solve it for small-amplitude monopole oscillations of the gas. The obtained damping rate is long enough to be neglected in a realistic cold-atom experiment, and therefore longitudinal trapping does not hinder integrable dynamics of atomic gases in the 1D regime.

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References

  1. 1.
    V.N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983)Google Scholar
  2. 2.
    T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2003)Google Scholar
  3. 3.
    H.B. Thacker, Rev. Mod. Phys. 53, 253 (1981)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    V.A. Yurovsky, M. Olshanii, D.S. Weiss, Adv. At. Mol. Opt. Phys. 55, 61 (2008)CrossRefGoogle Scholar
  5. 5.
    M. Rigol, V. Dunjko, V. Yurovsky, M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    C. Kollath, A.M. Läuchli, E. Altman, Phys. Rev. Lett. 98, 180601 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    D. Muth, B. Schmidt, M. Fleischhauer, New J. Phys. 12, 083065 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    M. Srednicki, Phys. Rev. E 50, 888 (1994)ADSCrossRefGoogle Scholar
  9. 9.
    M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    E.H. Lieb, W. Liniger, Phys. Rev. 130, 1605 (1963)MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    E.H. Lieb, Phys. Rev. 130, 1616 (1963)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    T. Kinoshita, T.R. Wenger, D.S. Weiss, Science 305, 1125 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    O. Morsch, M. Oberthaler, Rev. Mod. Phys. 78, 179 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    R. Folman, P. Krüger, D. Cassettari, B. Hessmo, T. Maier, J. Schmiedmayer, Phys. Rev. Lett. 84, 4749 (2000)ADSCrossRefGoogle Scholar
  15. 15.
    W. Hänsel, P. Hommelhoff, T.W. Hänsch, J. Reichel, Nature 413, 498 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    Y. Shin, C. Sanner, G.-B. Jo, T.A. Pasquini, M. Saba, W. Ketterle, D.E. Pritchard, M. Vengalattore, M. Prentiss, Phys. Rev. A 72, 021604(R) (2005)ADSCrossRefGoogle Scholar
  17. 17.
    J. Fortágh, C. Zimmermann, Rev. Mod. Phys. 79, 235 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    T. Kinoshita, T. Wenger, D.S. Weiss, Nature 440, 900 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    S. Hofferberth, I. Lesanovsky, T. Schumm, A. Imambekov, V. Gritsev, E. Demler, J. Schmiedmayer, Nature Phys. 4, 489 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    P. Krüger, S. Hofferberth, I.E. Mazets, I. Lesanovsky, J. Schmiedmayer, Phys. Rev. Lett. 105, 265302 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 65, 043614 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    A. Muryshev, G.V. Shlyapnikov, W. Ertmer, K. Sengstock, M. Lewenstein, Phys. Rev. Lett. 89, 110401 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    I.E. Mazets, T. Schumm, J. Schmiedmayer, Phys. Rev. Lett. 100, 210403 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    I.E. Mazets, J. Schmiedmayer, New J. Phys. 12, 055023 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    S. Tan, M. Pustilnik, L.I. Glazman, Phys. Rev. Lett. 105, 090404 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    I.E. Mazets, J. Schmiedmayer, Phys. Rev. A 79, 061603(R) (2009)ADSCrossRefGoogle Scholar
  27. 27.
    A. Minguzzi, D.M. Gangardt, Phys. Rev. Lett. 94, 240404 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    D. Guéry-Odelin, F. Zambelli, J. Dalibard, S. Stringari, Phys. Rev. A 60, 4851 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    E.P. Wigner, Phys. Rev. 98, 145 (1955)MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    V. Giovangigli, Multicomponent Flow Modeling (Birkhäuser, Boston, 1999)Google Scholar
  31. 31.
    L.P. Pitaevskii, E.M. Lifshitz, Physical Kinetics (Butterworth-Heinemann, Oxford, 1981)Google Scholar
  32. 32.
    P. Pedri, D. Guéry-Odelin, S. Stringari, Phys. Rev. A 68, 043608 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    M. Olshanii, Phys. Rev. Lett. 81, 938 (1998)ADSCrossRefGoogle Scholar
  34. 34.
    S. Stringari, Phys. Rev. Lett. 77, 2360 (1996)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Institute of Atomic and Subatomic PhysicsVienna University of TechnologyViennaAustria
  2. 2.Ioffe Physico-Technical InstituteSt. PetersburgRussia

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