Dark-bright solitons in Bose–Einstein condensates at finite temperatures

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.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]). It is important to note that, as shown in [17], the analytical results obtained in the framework of the 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. [29] for a review on the SGPE model. It should also be mentioned that while the above works chiefly considered finite-temperature effects for the case of a single dark soliton, the DGPE model and the anti-damping-incorporating ordinary differential equations (ODEs) for the soliton center were also examined in the case of multiple dark solitons. In particular, the cases of two and three oscillating and interacting anti-damped dark solitons were considered in [30].In this work, we study the finite-temperature dynamics of DB solitons in harmonically confined Bose gases. In particular, we adopt an effective mean-field description and analyze theoretically and numerically a system of two coupled DGPEs, describing the evolution of a binary quasi-one-dimensional (1D) BEC at finite temperature. We extend the considerations of [17] and develop a Hamiltonian perturbation theory for the two-component system at hand. This way, we obtain an equation of motion for the DB soliton center, similar to the one derived in [15,17]. This equation, which includes an anti-damping term accounting for finite temperature, provides a characteristic eigenvalue pair (i.e. a pair of solutions of the characteristic equation associated with the linear equation of motion), which is connected to the eigenvalue associated with the anomalous mode of the DB soliton. Performing a BdG analysis, we show that the anomalous mode eigenvalue becomes complex as the dissipation (temperature-dependent) parameter is introduced, leading to an instability of the DB soliton pair. The temperature dependence of the eigenvalues (determined analytically) is found to be in good agreement with the relevant anomalous mode eigenvalue (determined nu...

Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap

“…The dynamics of this third mode is found to correspond to an oscillating population imbalance between the two bright wave packets. This was first observed in the dissipative GPE framework (for DB pairs) of [23], where the third mode eigenfunction was added to the exact solution leading to the indicated imbalance. The out-of-phase bright components attract each other and in this case a negative energy linearization mode emerges that captures the tunneling of a fraction of the atoms from one atomic cloud (i.e., the one bright solitary wave) to the other.…”

Dynamics of dark-bright vector solitons in Bose-Einstein condensates

“…Although a bright soliton does not exist in a system with repulsive interactions [11], it can be supported in such a binary system due to the nonlinear interaction with the dark soliton component. These solitons can be referred to as symbiotic [6,12]. A similar possibility of such a mechanism was proposed early in the literature in terms of a Bose-Fermi mixture where bosons and fermions attract each other but the interaction between the bosons themselves is repulsive [13].…”

Stability and Dynamics of Dark-Bright Soliton Bound States Away from the Integrable Limit

“…A prototypical example of the latter is a coupled dark-bright (DB) soliton state in a highly elongated (quasi-one-dimensional) condensate cloud, consisting of a dark soliton in one component and a bright soliton in the second component of a binary BEC featuring intra-and inter-species repulsion. Since bright solitons are not self-sustained structures in repulsive (self-defocusing) media, DB solitons are often called symbiotic, that is the dark soliton can be thought of as acting as an effective potential well trapping the bright soliton [18][19][20][21][22]. Such symbiotic entities were first observed, and theoretically studied in the context of nonlinear optics [23][24][25][26][27][28][29][30][31][32].…”