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Chinese Physics

Dissipative dynamics of dark solitons in elongated Bose–Einstein condensates

Tang Zheng-Hua, Yan Jia-Ren, Linghong Liu

Published Aug 22, 2006• 1 citation
Publisher

Abstract

The dissipative dynamic stability is investigated of dark solitons in elongated Bose–Einstein condensates that can be described by the Gross–Pitaevskii equation including an additional term. Based on the direct perturbation theory for the nonlinear Schrodinger equation, the dependence of the soliton velocity on time is explicitly given, and the shape of dark solitons remaining unchanged under the dissipative condition is confirmed theoretically for the first time. It is found that the dynamically stable dark solitons turn out to be thermodynamically unstable.

DOI
10.1088/1009-1963/15/9/008

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The dissipative dynamic stability is investigated of dark solitons in elongated Bose–Einstein condensates that can be described by the Gross–Pitaevskii equation including an additional term. Based on the direct perturbation theory for the nonlinear Schrodinger equation, the dependence of the soliton velocity on time is explicitly given, and the shape of dark solitons remaining unchanged under the dissipative condition is confirmed theoretically for the first time. It is found that the dynamically stable dark solitons turn out to be thermodynamically unstable.
We study the stability and the attractor dynamics of an elongated Bose-Einstein condensate (BEC) with dark or gray kink solitons in the presence of localized dissipation. To this end, the three-dimensional Gross--Pitaevskii equation with an additional imaginary potential is solved numerically. We analyze the suppression of the snaking instability in dependence of the dissipation strength and extract the threshold value for the stabilization of the dark soliton for experimentally realistic parameters. Below the threshold value, we observe the decay into a solitonic vortex. Above the stabilization threshold, we observe the attractor dynamics towards the dark soliton when initially starting from a gray soliton. We find that for all initial conditions the dark soliton is the unique steady-state of the system---even when starting from the BEC ground state.
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.
We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.
We consider the dynamics of dark matter wave solitons moving through non-uniform cigar-shaped Bose–Einstein condensates described by the mean field Gross–Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose–Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic–quintic nonlinearity modelling two- and three-body interactions, respectively. Opposite to the usual (cubic) Gross–Pitaevskii equation for which the dark soliton effective mass is known to be constant (equal to 2), in the presence of a cubic–quintic nonlinearity we find that the effective mass depends on the product of the initial density background and the ratio between the coefficient of quintic and cubic nonlinearities, this leading to the interesting possibility of measuring three-body interactions directly from the dark soliton dynamics. A comparison between analytical results and direct numerical simulations of the cubic–quintic Gross–Pitaevskii equation shows good agreement between them which confirms the validity of our approach.