arXiv:1510.02223 · Physical Review A

Stable multiple vortices in collisionally inhomogeneous attractive Bose-Einstein condensates

J. B. Sudharsan, R. Radha, Henrique Fabrelli, A. Gammal, Boris A. Malomed

Published Nov 3, 2015• 13 citations

Abstract

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.

DOI: 10.1103/physreva.92.053601

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arXiv:1510.02223 · Physical Review A

Stable multiple vortices in collisionally inhomogeneous attractive Bose-Einstein condensates

J. B. Sudharsan, R. Radha, Henrique Fabrelli, A. Gammal, Boris A. Malomed

Published Nov 3, 2015• 13 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physreva.92.053601

Related papers

Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates

Lei Wu, Lu Li, Jie-Fang Zhang +3 more

We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in two-dimensional models of Bose-Einstein condensates with a spatially modulated nonlinearity of either sign and a harmonic trapping potential. The number of vortex-soliton (VS) modes is determined by the discrete energy spectrum of a related linear Schr\"odinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. Stable VSs with vorticity $S\ensuremath{\geqslant}2$ and those corresponding to higher-order radial states are reported, in the case of the attraction and repulsion, respectively.We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in two-dimensional models of Bose-Einstein condensates with a spatially modulated nonlinearity of either sign and a harmonic trapping potential. The number of vortex-soliton (VS) modes is determined by the discrete energy spectrum of a related linear Schr\"odinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. Stable VSs with vorticity $S\ensuremath{\geqslant}2$ and those corresponding to higher-order radial states are reported, in the case of the attraction and repulsion, respectively.

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arXiv:2502.09087Physical Review AFeb 21, 20256 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

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.

S\geq 2

and those corresponding to higher-order radial states are reported for the first time, in the case of the attraction and repulsion, respectively.

n

and

m

, corresponding to the transverse and circumferential directions, with the phase structure determined by the winding number (WN)

m

. Odd and even values of

n

must associate, respectively, with integer and half-integer values of

m

, the latter ones requiring two cycles of motion around MS for returning to the initial phase. Using variational and numerical methods, we solve the GP equation with the attractive nonlinearity, producing a family of ground-state (GS) solitons for values of the norm below the critical one, above which the collapse sets in. Vortex solitons with

n=1,m=1

and

n=2,m=1/2

are obtained in a numerical form. The vortex solitons with

n=1,m=1

are almost uniformly distributed in the azimuthal direction, while ones with

n=2,m=1/2

form localized states. The Vakhitov-Kolokolov criterion and linear-stability analysis for the GS soliton solutions and vortices with

n=1,m=1

demonstrates that they are completely stable, while the localized states with

n=2,m=1/2

are completely unstable. Finally, the motion of solitons on the MS and the collision of two solitons are discussed.