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arXiv:1404.7087 · Journal of Physics B Atomic Molecular and Optical Physics

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

S Gautam

Published Aug 6, 2014• 13 citations
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Abstract

We study the dynamics of a single and a corotating vortex pair in a dipolar Bose–Einstein condensate in the framework of a 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, 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.

DOI
10.1088/0953-4075/47/16/165301

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We study the dynamics of a single and a corotating vortex pair in a dipolar Bose–Einstein condensate in the framework of a 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, 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.
We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross--Pitaevskii equation, which is the Langevin equation for the Bose--Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.
In this paper, we study the dynamics of a single vortex and a corotating vortex pair in dipolar Bose-Einstein condensates under rotation.The results are obtained by numerically solving the nonlinear Gross-Pitaevskii equation.It is displayed that the dynamics behaviour is strongly dependent on the polarization angle and the rotation frequency.For a single vortex, the clockwise rotation occurs with an increasing rotation frequency, and the rotation direction is constant.The x coordinate and y coordinate as a function of time show that the single vortex is accelerated.The oscillation frequency is larger in the case of the totally repulsive dipolar interaction than for the anisotropic dipolar interaction.For a corotating vortex pair, the dynamic is different than in the case of a single vortex.When the rotation frequency is gradually increased, the corotating vortex pair spins from anti-clockwise to clockwise direction and the anisotropic dipolar interaction is fully embodied.In this process, the system has a critical rotation frequency to accomplish such transition.In addition, the vortex motion is confined to a small extent at this critical rotation frequency.These results reflect a competition between rotation and dipolar interaction.
In this paper, we examine the dynamical properties of vortices in atomic Bose-Einstein condensates in the presence of phenomenological dissipation, used as a basic model for the effect of finite temperatures. In the context of this so-called dissipative Gross-Pitaevskii model, we derive analytical results for the motion of single vortices and, importantly, for vortex dipoles, which have become very relevant experimentally. Our analytical results are shown to compare favorably to the full numerical solution of the dissipative Gross-Pitaevskii equation where appropriate. We also present results on the stability of vortices and vortex dipoles, revealing good agreement between numerical and analytical results for the internal excitation eigenfrequencies, which extends even beyond the regime of validity of this equation for cold atoms.
By numerically solving the Gross–Pitaevskii equation with phenomenological dissipation term, we study the vortex formation properties of a three-dimensional dipolar Bose–Einstein condensate of 164Dy atoms. We studied the influence of the contact interaction between atoms on the formation mechanism of vortices. We also study how the dipole orientation affects the vortex formation properties and the number of vortices. We find that enhancing the interaction of short-range repulsion interaction or dipolar repulsion interaction can shorten the time to form a stable vortex structure and increase the number of vortices.
Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. The log (base e) of total energy, trap energy, quantum energy, kinetic energy, internal energy and z-component of the angular momentum vs time were compared with f(x)=a+bx for that time when the vortices come in in the condensate. The increasing/decay rate of these energies and L_{z} were studied as a function of dissipation.
We study the influence of dipole–dipole interaction on the formation of vortices in a rotating dipolar Bose–Einstein condensate (BEC) of 52 Cr and 164 Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross–Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices, while a repulsive contact interaction increases the stability of the vortices. Furthermore, an ordered vortex lattice of a relatively large number of vortices is found in a strongly dipolar BEC.