TY - JOUR

T1 - Vortex stability in nearly-two-dimensional Bose-Einstein condensates with attraction

AU - Mihalache, Dumitru

AU - Mazilu, Dumitru

AU - Malomed, Boris A.

AU - Lederer, Falk

PY - 2006

Y1 - 2006

N2 - We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped Bose-Einstein condensate with negative scattering length. The analysis combines computation of the stability eigenvalues and direct simulations. The states with vorticity S=1 are stable in a third of their existence region, 0<N<(1 3) Nmax (S=1), where N is the number of atoms, and Nmax (S=1) is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, (13) Nmax (S=1) <N<0.43 Nmax (S=1), the unstable vortex periodically splits in twofragments and recombines. At N>0.43 Nmax (S=1), the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full three-dimensional (3D) Gross-Pitaevskii equation. In a moderately anisotropic 3D configuration, with the aspect ratio 10, the stability interval of the S=1 vortices occupies ≈40% of their existence region, hence the two-dimensional (2D) limit provides for a reasonable approximation in this case. For the isotropic 3D configuration, the stability interval expands to 65% of the existence domain. Overall, the vorticity heightens the actual collapse threshold by a factor of up to 2. All vortices with S≥2 are unstable.

AB - We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped Bose-Einstein condensate with negative scattering length. The analysis combines computation of the stability eigenvalues and direct simulations. The states with vorticity S=1 are stable in a third of their existence region, 0<N<(1 3) Nmax (S=1), where N is the number of atoms, and Nmax (S=1) is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, (13) Nmax (S=1) <N<0.43 Nmax (S=1), the unstable vortex periodically splits in twofragments and recombines. At N>0.43 Nmax (S=1), the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full three-dimensional (3D) Gross-Pitaevskii equation. In a moderately anisotropic 3D configuration, with the aspect ratio 10, the stability interval of the S=1 vortices occupies ≈40% of their existence region, hence the two-dimensional (2D) limit provides for a reasonable approximation in this case. For the isotropic 3D configuration, the stability interval expands to 65% of the existence domain. Overall, the vorticity heightens the actual collapse threshold by a factor of up to 2. All vortices with S≥2 are unstable.

UR - http://www.scopus.com/inward/record.url?scp=33646382408&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.73.043615

DO - 10.1103/PhysRevA.73.043615

M3 - מאמר

AN - SCOPUS:33646382408

VL - 73

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

M1 - 043615

ER -