Stability and dynamics of matter-wave vortices in the presence of collisional inhomogeneities and dissipative perturbations

Middelkamp, S.; Frantzeskakis, D. J.; Carretero-González, R.; Schmelcher, Peter

doi:10.1088/0953-4075/43/15/155303

Cited by 29 publications

(37 citation statements)

References 87 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More importantly for our theme of vortex dynamics, an increasing volume of literature has been exploring the role of thermal effects [47,48,49,50,51]. Here, too, and in accordance with theoretical predictions [52] (see also Ref.…”

supporting

confidence: 70%

Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation

Carretero-González

Kevrekidis

Kolokolnikov

2016

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential µ of the system, increasing proportionally to µ 2/3 . The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We show how these unstable modes typically nucleate a large number of vortices in the periphery of the atomic cloud. However, through a pattern selection mechanism, prompted by symmetry-breaking, only few isolated vortices are pulled in sequentially from the periphery towards the bulk of the cloud resulting in highly symmetric stable vortex configurations with far fewer vortices than the original unstable mode. These results may be of relevance to the experimentally tractable realm of finite temperature atomic condensates.

show abstract

supporting

confidence: 70%

Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation

Carretero-González

Kevrekidis

Kolokolnikov

2016

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…A natural direction to extend the present studies is to consider the higher dimensional setting of vortices [38] and of their two-component generalizations, namely the vortex-bright solitons [39]. Understanding the thermally induced dynamics and the modifications of the corresponding precessional motion, especially in the presence of multiple coherent structures, would constitute an interesting topic for future study.…”

Section: Discussionmentioning

confidence: 94%

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

2012

Self Cite

View full text Add to dashboard Cite

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...

show abstract

“…The suppression of the decay rate as the vortex moves closer to the trap center is also observed in condensates interacting via contact interactions [18,20]. In the absence of dissipation at T = 0 K, an off-center vortex traverses along an isoenergetic circular trajectory around the trap center due to the excitation of the anomalous or fundamental Kelvin mode [55][56][57]. The non-zero dissipation at finite temperatures slowly reduces the energy of the condensate, which is shown in Fig.…”

Section: Dynamics Of Vorticesmentioning

confidence: 96%

Dynamics of the corotating vortices in dipolar Bose–Einstein condensates in the presence of dissipation

Gautam¹

2014

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

We study the dynamics of a single and a corotating vortex pair in a dipolar Bose-Einstein condensate in the framework of dissipative Gross-Pitaevskii equation. This simple model enables us to simulate the effect of finite temperature on the vortex dynamics. We study the effect of dipolar interactions on the dynamics of a single vortex in the presence of phenomenological dissipation. In the case of a corotating vortex pair, an initial asymmetry in the locations of the vortices can lead to different decay rates for the constituent vortices as is the case for the condensates interacting via pure contact interactions. We observe that the anisotropic interaction between the component vortices manifests itself as the perceptible difference in the trajectories traversed by the vortices in the condensate at finite temperatures.

show abstract

Stability and dynamics of matter-wave vortices in the presence of collisional inhomogeneities and dissipative perturbations

Cited by 29 publications

References 87 publications

Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation

Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation

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

Dynamics of the corotating vortices in dipolar Bose–Einstein condensates in the presence of dissipation

Contact Info

Product

Resources

About