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Journal of Physics B Atomic Molecular and Optical Physics

Interaction of ring dark solitons with ring impurities in Bose–Einstein condensates

Ju-Kui Xue

Published Mar 8, 2005• 7 citations
Publisher

Abstract

The interaction of ring dark solitons/vortexes with the ring-shaped repulsive and attractive impurities in two-dimensional Bose–Einstein condensates is investigated numerically. Very rich interaction phenomena are obtained, i.e., not only the interaction between the ring soliton and the impurity, but also the interaction between vortexes and the impurity. The interaction characters, i.e., snaking of ring soliton, quasitrapping or reflection of ring soliton and vortexes by the impurity, strongly depend on initial ring soliton velocity, impurity strength, initial position of ring soliton and impurity. The numerical results also reveal that ring dark solitons/vortexes can be trapped and dragged by an adiabatically moving attractive ring impurity.

DOI
10.1088/0953-4075/38/6/006

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The interaction of ring dark solitons/vortexes with the ring-shaped repulsive and attractive impurities in two-dimensional Bose–Einstein condensates is investigated numerically. Very rich interaction phenomena are obtained, i.e., not only the interaction between the ring soliton and the impurity, but also the interaction between vortexes and the impurity. The interaction characters, i.e., snaking of ring soliton, quasitrapping or reflection of ring soliton and vortexes by the impurity, strongly depend on initial ring soliton velocity, impurity strength, initial position of ring soliton and impurity. The numerical results also reveal that ring dark solitons/vortexes can be trapped and dragged by an adiabatically moving attractive ring impurity.
We study the interaction of dark solitons with a localized impurity in Bose-Einstein condensates. We apply the soliton perturbation theory developed earlier in optics for describing the soliton dynamics and soliton-impurity interaction analytically, and then verify the results by direct numerical simulations of the Gross-Pitaevskii equation. We find that a dark soliton can be reflected from or transmitted through a repulsive impurity in a controllable manner, while near the critical point the soliton can be quasitrapped by the impurity. Additionally, we demonstrate that an immobile soliton may be captured and dragged by an adiabatically moving attractive impurity.
We investigate the dynamics and pattern formation of two ring dark solitons in a two-dimensional binary Bose-Einstein condensate with tunable intercomponent interaction via numerical simulation of the time-dependent Gross-Pitaevskii equation. Both the black and gray ring dark solitons are considered for cases where the modulation frequency of the intercomponent interaction is resonant or nonresonant with the one of the trapping potential. Our results show that in the presence of periodic modulation of the intercomponent interaction not only are the lifetimes of the ring dark solitons largely extended but also their decaying dynamics are dramatically affected. Before snaking instability sets in, new ring dark solitons are formed, and both the numbers and depths of the ring dark solitons exhibit collective oscillations. With the development of instability, the system exhibits different decaying processes, and a variety of decay profiles, such as vortex necklace, distorted octagon, vortex-antivortex ring, and cross, are formed, showing a strong dependence on the modulation frequency of the intercomponent interaction and the initial depth of the ring dark soliton.
By using a multiple-scale method, we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates. It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity, while at the position of the localized impurity the soliton can be quasitrapped by the impurity. Additionally, we find that the strength of the localized impurity has an important effect on the dark soliton dynamics. With increasing strength of the localized impurity, the amplitude of the dark soliton becomes bigger, while its width is narrower, and the soliton propagates slower.
We investigate both analytically and numerically the dynamics and modulation of ring dark solitons in two-dimensional Bose-Einstein condensates with tunable interaction. The analytic solutions for the ring dark soliton are derived by using a transformation method. A shallow ring dark soliton is stable when the ring is slightly distorted, while for large deformation of the ring, vortex pairs appear and demonstrate different dynamical behaviors: the vortex pairs transform into dark lumplike solitons and revert to ring dark solitons periodically. Moreover, our results show that the dynamical evolution of the ring dark soliton can be dramatically affected by the Feshbach resonance, and the lifetime of the ring dark soliton can be greatly extended, which offers a useful method for observing ring dark solitons in future experiments.
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.