TY - JOUR

T1 - On stability of vortices in three-dimensional self-attractive Bose-Einstein condensates

AU - Malomed, Boris A.

AU - Lederer, Falk

AU - Mazilu, Dumitru

AU - Mihalache, Dumitru

N1 - Funding Information:
Support from Deutsche Forschungsgemeinschaft (DFG), Bonn, is acknowledged. The work of B.A.M. was partially supported by the Israel Science Foundation through the Center-of-Excellence grant No. 8006/03.

PY - 2007/2/5

Y1 - 2007/2/5

N2 - Results of accurate analysis of stability are reported for localized vortices in the Bose-Einstein condensate (BEC) with the negative scattering length, trapped in an anisotropic potential with the aspect ratio sqrt(Ω). The cases of Ω ≫ 1 and Ω ≪ 1 correspond to the "pancake" (nearly-2D) and "cigar-shaped" (nearly-1D) configurations, respectively (in the latter limit, the vortices become "tubular" solitons). The analysis is based on the 3D Gross-Pitaevskii equation. The family of solutions with vorticity S = 1 is accurately predicted by the variational approximation. The relative size of the stability area for the vortices with S = 1 (which was studied, in a part, before) increases with the decrease of Ω in terms of the number of atoms, but decreases in terms of the chemical potential. All states with S ≥ 2 are unstable, while the stability of the ordinary solitons (S = 0) obeys the Vakhitov-Kolokolov criterion. The stability predictions are verified by direct simulations of the full 3D equation.

AB - Results of accurate analysis of stability are reported for localized vortices in the Bose-Einstein condensate (BEC) with the negative scattering length, trapped in an anisotropic potential with the aspect ratio sqrt(Ω). The cases of Ω ≫ 1 and Ω ≪ 1 correspond to the "pancake" (nearly-2D) and "cigar-shaped" (nearly-1D) configurations, respectively (in the latter limit, the vortices become "tubular" solitons). The analysis is based on the 3D Gross-Pitaevskii equation. The family of solutions with vorticity S = 1 is accurately predicted by the variational approximation. The relative size of the stability area for the vortices with S = 1 (which was studied, in a part, before) increases with the decrease of Ω in terms of the number of atoms, but decreases in terms of the chemical potential. All states with S ≥ 2 are unstable, while the stability of the ordinary solitons (S = 0) obeys the Vakhitov-Kolokolov criterion. The stability predictions are verified by direct simulations of the full 3D equation.

UR - http://www.scopus.com/inward/record.url?scp=33845458391&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2006.09.054

DO - 10.1016/j.physleta.2006.09.054

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AN - SCOPUS:33845458391

SN - 0375-9601

VL - 361

SP - 336

EP - 340

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 4-5

ER -