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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S.N. Bose, Zeitschrift Phys. 26, 178 (1924)
A. Einstein, Sitzungsberichte der Preussischen Akademie der Wissenschaften (1924)
M.A. Anderson, B.P. Kasevich, Science 282, 1686 (1998)
K. Burnett, Contemp. Phys. 37, 1 (1996)
A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)
L. Khaykovich et al., Science 296, 1290 (2002)
K.E. Strecker et al., Nature 417, 150 (2002)
B.B. Baizakov et al., Europhys. Lett. 63, 642 (2003)
D. Mihalache et al., Phys. Rev. A 72, 021601 (2005)
B. Lemesurier, P. Christiansen, Phys. D 184, 226 (2003)
B.J. Lemesurier et al., Phys. Rev. E 70, 046614 (2004)
J. Reichel, App. Phys. B 74, 469 (2002)
R. Folman et al., Adv. At. Mol. Opt. Phys. 48, 263 (2002)
R. Grimm et al., Adv. At. Mol. Opt. Phys. 42, 95 (2000)
R. Fedele et al., JETP Lett. 80, 535 (2004)
S. de Nicola et al., Eur. Phys. J. B 54, 113 (2006)
S.N. Vlasov et al., Radiophys. Quant. Electr. 14, 1062 (1971)
J.J. Rasmussen, K. Rypdal, Phys. Scr. 33, 481 (1986)
P.A. Robinson, Rev. Mod. Phys. 69, 507 (1997)
S.K. Turitsyn, Phys. Rev. E 47, 13 (1993)
E.A. Kuznetsov et al., Phys. D 87, 273 (1995)
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Movies 1: Temporal dependence of the perpendicular wavefunctions, |ψ⊥|² and |ψ⊥1|² (dashed and solid lines, respectively). The maximum time of the movie is tmax = 24.
Movies 2: Temporal evolution of the potential |ψ| for repulsive interactions, β = -1. Other parameters are adopted as a = 1.5, C = 1.58, k = 0, γ0 = 0, σ0 = 1, γ1 = 0.05, σ1 = 0.95, α⊥ = 0.9, α|| = 1.15, λ⊥ = 0.9, λ|| = 1.2, τ⊥ = 1.15 and τ|| = 1.3. The maximum time of the movie is tmax = 24.
Movie 3: Temporal evolution of the potential |ψ| for weak attractive interactions, β = +0.15. Other parameters are the same as in Fig. 2. The maximum time is tmax = 24.
Movie 4: Temporal evolution of the potential |ψ| for stronger attractive interactions, β = +1. Other parameters are the same as in Fig. 2. The maximum time is tmax = 3.2.
Rights and permissions
About this article
Cite this article
Jovanović, D., Fedele, R. Stability of two-dimensional, controlled, Bose-Einstein coherent states . Eur. Phys. J. B 60, 363–368 (2007). https://doi.org/10.1140/epjb/e2007-00361-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2007-00361-6