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Acta Physica Polonica A

Numerical Study of Vortex Dynamics in Dipolar Bose Atomic Gases

Qiang Zhao, Hongjing Bi, Xiao-Meng Yang, Lili Zhang

Published Jun 1, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.141.578

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AIP conference proceedings•Jan 1, 2020•0 citations
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.
Based on the two-dimensional mean-field equations for pancake-shaped dipolar Bose-Einstein condensates in a rotating frame, for both attractive and repulsive dipole-dipole interaction (DDI) as well as arbitrary polarization direction, we study the profiles of the single vortex state and show how the critical rotational frequency changes with the sss-wave contact interaction strength, DDI strength, and polarization angle. In addition, we find numerically that at the ``magic angle'' $\ensuremath{\vartheta}=arccos(\sqrt{3}/3)$, the critical rotational frequency is almost independent of the DDI strength. By numerically solving the dipolar Gross-Pitaevskii equation at high rotation speed, we identify different patterns of vortex lattices which strongly depend on the polarization direction. As a result, we undergo a study of vortex lattice structures for the whole regime of polarization direction and find evidence that the vortex lattice orientation tends to be aligned to the dipole polarization axis for positive DDI strength and to the perpendicular direction of the dipole axis for negative DDI strength.
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 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.
We study the formation and dynamics of vortices in quasi two-dimensional dipolar Bose-Einstein condensates (BECs). We solve the time dependent two-dimensional Gross-Pitaevskii equation by using a combined split-step Crank-Nicolson (SSCN) and Fast Fourier-Transform (FFT) based numerical scheme and investigate the vortex dynamics in dipolar BECs trapped with harmonic and optical lattice potentials. The consequence of dipole-dipole interaction on vortex nucleation and number of vortices has been analysed. We observe that the breaking of symmetry due to anisotropic dipolar interaction enormously increase the speed of creation of vortices.
We present full three-dimensional numerical calculations of single vortex states in rotating dipolar condensates. We consider a Bose-Einstein condensate of 52Cr^{52}\text{C}\text{r}52Cr atoms with dipole-dipole and sss-wave contact interactions confined in an axially symmetric harmonic trap. We obtain the vortex states by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. We investigate the properties of a single vortex and calculate the critical angular velocity for different values of the sss-wave scattering length. We show that, whereas the standard variational approach breaks down in the limit of pure dipolar interactions, exact solutions of the Gross-Pitaevskii equation can be obtained for values of the sss-wave scattering length down to zero. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis for different values of the angular velocity of the rotating trap.
We investigate the impact of interplay between the contact interaction and the dipole-dipole interaction on the rotational properties of dipolar Bose-Einstein condensate, rotating in an axially confined double-well potential. The dynamics is governed by a quasi-two-dimensional Gross-Pitaevskii equation with phenomenological dissipation and non-local dipole-dipole interaction integral. In the present study, we consider using three different dipolar atoms namely 52Cr, 168Er and 164Dy with increasing order of dipole-dipole interaction strength respectively. From our numerical simulation, we see, at the critical frequency, the vortex core starts to emerge from the peripheries of the BEC. Further, we observe that the critical frequency of vortex nucleation decreases with an increase of dipole-dipole interaction strength and contact interaction strength and these interactions also enhance the number of vortices. We also find that the increase in average angular momentum per atom with rotational frequency suddenly shifts from linear to non-linear progression after attaining the critical rotational frequency. From the results obtained in the present study, it is quite clear that dipole-dipole interaction and contact interaction compliments with each other, has a considerable influence on the rotational properties of dipolar BECs.