We study the stability of solitary vortices in a two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov--de Gennes equations and running direct simulations of the underlying Gross-Pitaevskii equation reveals that vortices with a topological charge up to $S=6$ (at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with $S$ ). The largest nonlinearity-localization radius admitting stabilization of higher-order vortices is estimated analytically and accurately identified in numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices, $S>1$ , in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.We study the stability of solitary vortices in a two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov--de Gennes equations and running direct simulations of the underlying Gross-Pitaevskii equation reveals that vortices with a topological charge up to $S=6$ (at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with $S$). The largest nonlinearity-localization radius admitting stabilization of higher-order vortices is estimated analytically and accurately identified in numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices, $S>1$, in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.

arXiv:1510.02223Physical Review ANov 3, 201513 citations

Multicharged vortices stability in Bose-Einstein condensates

A. Cidrim, F. E. A. dos Santos, Vanderlei Salvador Bagnato

Abstracts BookJan 1, 20140 citations

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

DUMITRU BOGDAN MIHALACHE, Dumitru Mazilu, Boris A. Malomed +1 more

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, $0<N<(1∕3){N}_{\mathrm{max}}^{(S=1)}$ , where $N$ is the number of atoms, and ${N}_{\mathrm{max}}^{(S=1)}$ is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, $(1∕3){N}_{\mathrm{max}}^{(S=1)}<N<0.43{N}_{\mathrm{max}}^{(S=1)}$ , the unstable vortex periodically splits in twofragments and recombines. At $N>0.43{N}_{\mathrm{max}}^{(S=1)}$ , 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 $\sqrt{10}$ , the stability interval of the $S=1$ vortices occupies $\ensuremath{\approx}40%$ 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 $S\ensuremath{\geqslant}2$ are unstable.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, $0<N<(1∕3){N}_{\mathrm{max}}^{(S=1)}$, where $N$ is the number of atoms, and ${N}_{\mathrm{max}}^{(S=1)}$ is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, $(1∕3){N}_{\mathrm{max}}^{(S=1)}<N<0.43{N}_{\mathrm{max}}^{(S=1)}$, the unstable vortex periodically splits in twofragments and recombines. At $N>0.43{N}_{\mathrm{max}}^{(S=1)}$, 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 $\sqrt{10}$, the stability interval of the $S=1$ vortices occupies $\ensuremath{\approx}40%$ 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 $S\ensuremath{\geqslant}2$ are unstable.

arXiv:cond-mat/0603793Physical Review AApr 26, 2006120 citations

Vortices in two-dimensional Bose-Einstein condensates

Shuxing Chen, Shing–Tung Yau

AMS/IP studies in advanced mathematicsSep 3, 20022 citations

Formation of vortices in a three-dimensional dipolar Bose-Einstein condensate

Yuan Sheng Wang, Shen Tong Ji, Yue E. Luo +1 more

We investigate the vortex formation properties of a three-dimensional (3D) dipolar Bose-Einstein condensate (BEC) of 52 Cr atoms in an optical lattice potential through numerical simulations of the time-dependent Gross-Pitaevskii equation with a dissipation term. The mechanisms that influence the dipole-dipole interaction and the repulsive contact interaction between atoms during vortex formation are analyzed. We find that the stability of the vortices weakens with increasing attractive dipolar strength and that the repulsive contact interaction between atoms can increase the number of vortices.We investigate the vortex formation properties of a three-dimensional (3D) dipolar Bose-Einstein condensate (BEC) of 52 Cr atoms in an optical lattice potential through numerical simulations of the time-dependent Gross-Pitaevskii equation with a dissipation term. The mechanisms that influence the dipole-dipole interaction and the repulsive contact interaction between atoms during vortex formation are analyzed. We find that the stability of the vortices weakens with increasing attractive dipolar strength and that the repulsive contact interaction between atoms can increase the number of vortices.

Journal of the Korean Physical SocietyNov 1, 20154 citations

S=6

(at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with

S

). The largest nonlinearity-localization radius admitting stabilization of higher-order vortices is estimated analytically and accurately identified in numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices,

S>1

, in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.

S=1

are stable in a third of their existence region,

0<N<(1∕3){N}_{\mathrm{max}}^{(S=1)}

, where

N

is the number of atoms, and

{N}_{\mathrm{max}}^{(S=1)}

is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval,

(1∕3){N}_{\mathrm{max}}^{(S=1)}<N<0.43{N}_{\mathrm{max}}^{(S=1)}

, the unstable vortex periodically splits in twofragments and recombines. At

N>0.43{N}_{\mathrm{max}}^{(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

\sqrt{10}

, the stability interval of the

S=1

vortices occupies $\ensuremath{\approx}40%$ 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 $S\ensuremath{\geqslant}2$ are unstable.