The European Physical Journal B

, Volume 60, Issue 3, pp 363–368 | Cite as

Stability of two-dimensional, controlled, Bose-Einstein coherent states

Statistical and Nonlinear Physics

Abstract.

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schrödinger soliton [JETP Lett. 80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically, taking initialy a controlled soliton whose “effective mass” is several times bigger than the critical value for a weak collapse in the absence of a potential well, and allowing for reasonably large errors in the experimental realization of the trapping potential required by the theory. For repulsive and sufficiently weak attractive interactions, the controlled state is shown to remain stable inside a breathing potential well, for a time that is an order of magnitude longer than the characteristic periods of the forced and eigenoscillations of the soliton. The collapse is observed only for attractive interactions, when the nonlinear attraction exceeded the appropriate threshold.

PACS.

03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations 05.45.Yv Solitons 05.30.Jp Boson systems 

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Supplementary material

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References

  1. S.N. Bose, Zeitschrift Phys. 26, 178 (1924) CrossRefADSGoogle Scholar
  2. A. Einstein, Sitzungsberichte der Preussischen Akademie der Wissenschaften (1924) Google Scholar
  3. M.A. Anderson, B.P. Kasevich, Science 282, 1686 (1998) CrossRefADSGoogle Scholar
  4. K. Burnett, Contemp. Phys. 37, 1 (1996) CrossRefADSMathSciNetGoogle Scholar
  5. A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001) CrossRefADSGoogle Scholar
  6. L. Khaykovich et al., Science 296, 1290 (2002) CrossRefGoogle Scholar
  7. K.E. Strecker et al., Nature 417, 150 (2002) CrossRefGoogle Scholar
  8. B.B. Baizakov et al., Europhys. Lett. 63, 642 (2003) CrossRefADSGoogle Scholar
  9. D. Mihalache et al., Phys. Rev. A 72, 021601 (2005) CrossRefADSGoogle Scholar
  10. B. Lemesurier, P. Christiansen, Phys. D 184, 226 (2003) MATHCrossRefMathSciNetGoogle Scholar
  11. B.J. Lemesurier et al., Phys. Rev. E 70, 046614 (2004) CrossRefADSGoogle Scholar
  12. J. Reichel, App. Phys. B 74, 469 (2002) CrossRefADSGoogle Scholar
  13. R. Folman et al., Adv. At. Mol. Opt. Phys. 48, 263 (2002) Google Scholar
  14. R. Grimm et al., Adv. At. Mol. Opt. Phys. 42, 95 (2000) CrossRefGoogle Scholar
  15. R. Fedele et al., JETP Lett. 80, 535 (2004) CrossRefADSGoogle Scholar
  16. S. de Nicola et al., Eur. Phys. J. B 54, 113 (2006) CrossRefADSGoogle Scholar
  17. S.N. Vlasov et al., Radiophys. Quant. Electr. 14, 1062 (1971) CrossRefADSGoogle Scholar
  18. J.J. Rasmussen, K. Rypdal, Phys. Scr. 33, 481 (1986) MATHCrossRefADSMathSciNetGoogle Scholar
  19. P.A. Robinson, Rev. Mod. Phys. 69, 507 (1997) CrossRefADSGoogle Scholar
  20. S.K. Turitsyn, Phys. Rev. E 47, 13 (1993) CrossRefADSMathSciNetGoogle Scholar
  21. E.A. Kuznetsov et al., Phys. D 87, 273 (1995) CrossRefMathSciNetGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institute of PhysicsBelgradeSerbia
  2. 2.Dipartimento di Scienze FisicheUniversità Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. AngeloNapoliItaly

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