Laser Physics

, Volume 20, Issue 3, pp 671–677 | Cite as

Bose-Einstein condensate in a double well potential in the vicinity of a critical point

  • B. Oleś
  • P. Ziń
  • J. Chwedeńczuk
  • K. Sacha
  • M. Trippenbach
Physics of Cold Trapped Atoms

Abstract

We consider a Bose-Einstein condensate with an attractive particle interaction in a symmetric double well potential. It is known that in the mean field description a symmetric solution for the condensate wavefunction becomes unstable when the interactions are stronger than some critical value. We analyze the system around the critical point applying the number conserving Bogoliubov theory and exact diagonalization of the two mode hamiltonian. It allows for estimation of the density fluctuations in the system. Fluctuations of the order parameter, which is defined in the mean field description, turn out to be maximal at the critical point.

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References

  1. 1.
    S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Phys. Rev. A 59, 620 (1999); E. A. Ostrovskaya, Y.S. Kivshar, M. Lisak, B. Hall, F. Cattani, and D. Anderson Phys. Rev. A 61, 031601 (R) (2000).CrossRefADSGoogle Scholar
  2. 2.
    K. W. Mahmud, J. N. Kutz, and W. P. Reinhardt, Phys. Rev. A 66, 063607 (2002); P. Zin, E. Infeld, M. Matuszewski, G. Rowlands, and M. Trippenbach, Phys. Rev. A 73, 022105 (2006); E. Infeld, P. Zin, J. Gocalek, and M. Trippenbach, Phys. Rev. E 74, 026610 (2006).CrossRefADSGoogle Scholar
  3. 3.
    J. I. Cirac, M. Lewenstein, K. Mølmer, and P. Zoller, Phys. Rev. A 57, 1208 (1998); J. Ruostekoski, M. J. Collett, R. Graham, and D. F. Walls, Phys. Rev. A 57, 511 (1998); D. Gordon and C. M. Savage, Phys. Rev. A 59, 4623 (1999); D. A. R. Dalvit, J. Dziarmaga, and W. H. Zurek, Phys. Rev. A 62, 013607 (2000); A. Micheli, D. Jaksch, J. I. Cirac, and P. Zoller, Phys. Rev. A 67, 013607 (2003).CrossRefADSGoogle Scholar
  4. 4.
    Z. P. Karkuszewski, K. Sacha, and A. Smerzi, Eur. Phys. J. D 21, 251 (2002); B. Wu, R. B. Diener, and Q. Niu, Phys. Rev. A 65, 025601 (2002); D. Witthaut, E. M. Graefe, and J. Korsch, Phys. Rev. A 73, 063609 (2006).CrossRefADSGoogle Scholar
  5. 5.
    L. Pitaevskii and S. Stringari, Phys. Rev. Lett. 87, 180402 (2001).CrossRefADSGoogle Scholar
  6. 6.
    M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Phys. Rev. Lett. 95, 110405 (2005); R. Gati, B. Hemmerling, J. Fölling, M. Albiez, and M. K. Oberthaler, Phys. Rev. Lett. 96, 130404 (2006).CrossRefGoogle Scholar
  7. 7.
    For a topical review see R. Gati and M. Oberthaler, J. Phys. B 40, R61 (2007) and references therein.CrossRefADSGoogle Scholar
  8. 8.
    R. Kanamoto, H. Saito, and M. Ueda, Phys. Rev. A 73, 033611 (2006).CrossRefADSGoogle Scholar
  9. 9.
    G. J. Milbum, J. Corney, E. M. Wright, and D. P. Walls, Phys. Rev. A 55, 4318 (1997).CrossRefADSGoogle Scholar
  10. 10.
    R. Botet and R. Jullien, Phys. Rev. B 28, 3955 (1983).CrossRefADSGoogle Scholar
  11. 11.
    P. Ziń, J. Chwedeńczuk, B. Oleś, K. Sacha, and M. Trippenbach, EPL 83, 64007 (2008).CrossRefADSGoogle Scholar
  12. 12.
    M. D. Girardeau and R. Arnowitt, Phys. Rev. 113, 755 (1959); C. W. Gardiner, Phys. Rev. A 56, 1414 (1997); M. D. Girardeau, Phys. Rev. A 58, 775 (1998).MATHCrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Y. Castin and R. Dum, Phys. Rev. A 57, 3008 (1998); Y. Castin, in Les Houches Session, LXXII, Coherent Atomic Matter Waves 1999, Ed. by R. Kaiser, C. Westbrook, and F. David (Springer, Berlin, Heilderberg, New York, 2001).CrossRefADSGoogle Scholar
  14. 14.
    A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001).CrossRefADSGoogle Scholar
  15. 15.
    J. Dziarmaga and K. Sacha, Phys. Rev. A 67, 033608 (2003); J. Dziarmaga and K. Sacha, J. Phys. B 39, 57 (2006).CrossRefADSGoogle Scholar
  16. 16.
    B. Oleś and K. Sacha, J. Phys. A 41, 145005 (2008).CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • B. Oleś
    • 1
  • P. Ziń
    • 2
  • J. Chwedeńczuk
    • 3
    • 4
  • K. Sacha
    • 1
  • M. Trippenbach
    • 2
    • 3
  1. 1.Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research CentreJagicllonian UniversityKrakówPoland
  2. 2.Soltan Institute for Nuclear StudiesWarsawPoland
  3. 3.Institute for Theoretical PhysicsWarsaw UniversityWarsawPoland
  4. 4.BEC-CNR-INFM and Dipartimento di FisicaUniversita di TrentoPovoItaly

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