Advertisement

One-dimensional cubic-quintic Gross-Pitaevskii equation for Bose-Einstein condensates in a trap potential

  • Carlos Trallero-Giner
  • Rolci CipolattiEmail author
  • Timothy C. H. Liew
Regular Article

Abstract

By means of a new variational method we report a direct solution for quintic and cubic-quintic nonlinear 1D Gross-Pitaeskii equations (GPE) in a harmonic confined potential. We explore the influence of the quintic nonlinear term on the ideal 1D pure cigar-like shape model for attractive and repulsive atom-atom interaction in Bose-Einstein condensates (BEC). Also, we offer a closed analytical expression to evaluate the error produced when solely the cubic nonlinear GPE is considered in the description of 1D BEC.

Keywords

Cold Matter and Quantum Gas 

References

  1. 1.
    A. Görlitz et al., Phys. Rev. Lett. 87, 130402 (2001)CrossRefGoogle Scholar
  2. 2.
    M. Greiner, I. Bloch, O. Mandel, T.W. Hänsch, T. Esslinger, Phys. Rev. Lett. 87, 160405 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    F.S. Cataliotti et al., Science 293, 843 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    E.H. Lieb, Phys. Rev. 130, 1616 (1963)MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    M. Olshanii, Phys. Rev. Lett. 81, 938 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    D.S. Petrov, G.V. Shlyapnikov, J.T.M. Walraven, Phys. Rev. Lett. 85, 3745 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    E.H. Lieb, R. Seiringer, J. Yngvason, Commun. Math. Phys. 244, 347 (2004)MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    A.B. Tacla, C.M. Caves, Phys. Rev. A 84, 053606 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    A.E. Muryshev, G.V. Shlyapnikov, W. Ertmer, K. Sengstock, M. Lewenstein, Phys. Rev. Lett. 89, 110401 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    L. Khaykovich, B.A. Malomed, Phys. Rev. Lett. 74, 023607 (2006)ADSGoogle Scholar
  11. 11.
    R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis, Nonlinearity 21, R139 (2008)ADSzbMATHCrossRefGoogle Scholar
  12. 12.
    A.E. Muryshev, G.V. Shlyapnikov, W. Ertmer, K. Sengstock, M. Lewenstein, Phys. Rev. Lett. 89, 110401 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    L. Khaykovich, B.A. Malomed, Phys. Rev. A 74, 023607 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    H. Al-Jibbouri, I. Vidanović, A. Balaz, A. Pelster, arXiv: 1208.0991v1Google Scholar
  16. 16.
    Kh.I. Pushkarov, D.I. Pushkarov, I.V. Tomov, Opt. Quantum Electron. 11, 471 (1979)ADSCrossRefGoogle Scholar
  17. 17.
    S. Sinha, A.Y. Cherny, D. Kovrizhin, J. Brand, Phys. Rev. Lett. 96, 030406 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 65, 043614 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    Y.V. Kartashov, B.A. Malomed, L. Torner, Rev. Mod. Phys. 83, 247 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    J. Zeng, B.A. Malomed, Phys. Rev. A 85, 023824 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    V.M. Pérez-García, H. Michinel, H. Herrero, Phys. Rev. A 57, 3837 (1998)ADSCrossRefGoogle Scholar
  22. 22.
    A. Gammal, L. Tomio, T. Frederico, Phys. Rev. A 66, 043619 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    L.D. Carr, Y. Castin, Phys. Rev. A 66, 063602 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    R. Carles, Ann. Henri Poincar3é, 757 (2002)Google Scholar
  25. 25.
    Y.-G. Oh, J. Diff. Equations 81, 255 (1989)zbMATHCrossRefGoogle Scholar
  26. 26.
    R. Cipolatti, J. López Gondar, C. Trallero-Giner, Physica D: Nonlinear Phenomena 241, 755 (2012)ADSzbMATHCrossRefGoogle Scholar
  27. 27.
    T. Cazenave, Semilinear Schrödinger Equations. Courant Lecture Notes in Mathematics (American Mathematical Society, Providence, 2003), Vol. 10, p. 323Google Scholar
  28. 28.
    E. Zeidler, Nonlinear Functional Analysis and its Applications (Springer-Verlag, 1993), Vol. 1, p. 909Google Scholar
  29. 29.
    C. Trallero-Giner, T.H.C. Liew, A.V. Kavokin, Phys. Rev. B 82, 165421 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    E.H. Lieb, R. Seiringer, J. Yngvason, Phys. Rev. Lett. 91, 150401 (2003)ADSCrossRefGoogle Scholar
  31. 31.
    V.A. Brazhnyi, V.V. Konotop, L.P. Pitaevskii, Phys. Rev. A 73, 053601 (2006)ADSCrossRefGoogle Scholar
  32. 32.
    C. Trallero-Giner, V. Lopez-Richard, M.-Ch. Chung, A. Buchleitner, Phys. Rev. A 79, 063621 (2009)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Carlos Trallero-Giner
    • 1
  • Rolci Cipolatti
    • 2
    Email author
  • Timothy C. H. Liew
    • 3
  1. 1.Centro Brasileiro de Pesquisas FísicasRio de JaneiroBrazil
  2. 2.Universidade Federal do Rio de JaneiroRio de JaneiroBrazil
  3. 3.Mediterranean Institute of Fundamental PhysicsRomeItaly

Personalised recommendations