Abstract
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.
Highlights
Macroscopic nonlinear excitations of atomic Bose-Einstein condensates (BECs) [1, 2] have been a subject of intense theoretical and experimental research over the last few years [3]
Of particular interest are coupled dark-bright (DB) solitons that may exist in binary mixtures of BECs with repulsive interatomic interactions: these solitons are frequently called symbiotic ones, as the bright soliton component can be supported due to the nonlinear coupling with the dark soliton component
It is important to note that, as shown in Ref. [17], the analytical results obtained in the framework of the dissipative Gross-Pitaevskii equation (DGPE) were found to be in very good agreement with numerical results obtained in the framework of the stochastic Gross-Pitaevskii equation (SGPE); see, e.g., Ref. [29] for a review on the SGPE model
Summary
Macroscopic nonlinear excitations of atomic Bose-Einstein condensates (BECs) [1, 2] have been a subject of intense theoretical and experimental research over the last few years [3]. [17] by applying the Hamiltonian approach of the perturbation theory for dark matter-wave solitons [6] to the so-called dissipative Gross-Pitaevskii equation (DGPE) This model incorporates a damping term (accounting for finite temperature), first introduced phenomenologically by Pitaevskii [27], and later shown to be relevant from a microscopic perspective (see, e.g., the review [28]). Our analytical considerations and numerical results reveal a fundamental effect: the partial stabilization that the bright (“filling”) soliton component offers to the corresponding “bare” dark soliton against temperature-induced anti-damping This way, a significantly longer lifetime of the symbiotic (dark-bright) structure can be achieved, in comparison to its bare dark soliton counterpart.
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