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arXiv:cond-mat/0404150 · Physical Review Letters

Vortex-Line Solitons in A Periodically Modulated Bose-Einstein Condensate

J.-P. Martikainen, Henk T. C. Stoof

Published Aug 13, 2004• 8 citations
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Abstract

We study the nonlinear excitations of a vortex line in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the classical Euler dynamics of the vortex results in a description of the vortex line in terms of a (discrete) one-dimensional Gross-Pitaevskii equation, which allows for both bright and gray soliton solutions. We discuss these solutions in detail and predict that it is possible to create vortex-line solitons with current experimental capabilities.

DOI
10.1103/physrevlett.93.070402

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We studied the evolution of vortex solitons in two-component coupled Bose-Einstein condensates trapped in a harmonic potential. Using a two-dimensional coupled Gross-Pitaevskii equation model and a variational method, we theoretically derived the vortex soliton solution. Under an appropriate parametric setting, the derived vortex soliton radius was found to oscillate periodically. The derived quasi-stable states with typical nonlinear features are pictorially demonstrated and can be used to guide relevant experimental observations of vortex soliton phenomena in coupled ultracold atomic systems.
We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in 2D 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 Schrödinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. \emph{% Stable} VSs with vorticity S≥2S\geq 2S≥2 and those corresponding to higher-order radial states are reported for the first time, in the case of the attraction and repulsion, respectively.
Soliton is an exotic topological excitation, and it widely exists in various nonlinear systems, such as nonlinear optics, Bose-Einstein condensates, classical and quantum fluids, plasma, magnetic materials, etc. A stable soliton can propagate with constant amplitude and velocity, and maintain its shape. Two-dimensional and three-dimensional solitons are usually hard to stabilize, and how to realize stable two-dimensional or three-dimensional solitons has aroused the great interest of the researchers. Ring dark soliton is a kind of two-dimensional soliton, which was first theoretically predicted and experimentally realized in nonlinear optical systems. Compared with the usual two-dimensional solitons, ring dark solitons have good stability and rich dynamical behaviors. Owing to their highly controllable capability, Bose-Einstein condensates provide a new platform for studying the ring dark solitons. Based on the recent progress in Bose-Einstein condensates and solitons, this paper reviews the research on the analytic solutions, stability, as well as the decay dynamics of ring dark solitons in Bose-Einstein condensates. A transform method is introduced, which generalizes the analytic solutions of ring dark solitons from a homogeneous system with time-independent nonlinearity to a harmonically trapped inhomogeneous system with time-dependent nonlinearity. The stability phase diagram of the ring dark soliton under deformation perturbations is discussed by numerically solving the Gross-Pitaevskii equations in the mean-field theory. A method of enhancing the stability of ring dark solitons by periodically modulating the nonlinear coefficients is introduced. It is also shown that the periodically modulated nonlinear coefficient can be experimentally realized by the Feshbach resonance technology. In addition, we discuss the dynamics of the decay of ring dark solitons. It is found that the ring dark soliton can decay into various vortex clusters composed of vortices and antivortices. This opens a new avenue to the investigation of vortex dynamics and quantum turbulence. It is also found that the ring dark solitons combined with periodic modulated nonlinearity can give rise to the pattern formation, which is an interesting nonlinear phenomenon widely explored in all the fields of nature. Finally, some possible research subjects about ring dark solitons in future research are also discussed.
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