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arXiv:1506.08184 · Journal of Physics B Atomic Molecular and Optical Physics

Three-dimensional vortex structures in a rotating dipolar Bose–Einstein condensate

Ramavarmaraja Kishor Kumar, Thangarasu Sriraman, Henrique Fabrelli, Paulsamy Muruganandam, Arnaldo Gammal

Published Jul 5, 2016• 21 citations
arXivHTMLPDF

Abstract

Abstract We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio ( λ ) and dipole–dipole interaction strength ( D ) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.

DOI
10.1088/0953-4075/49/15/155301

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Abstract We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio ( λ ) and dipole–dipole interaction strength ( D ) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.
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 examine the vortex formation and vortex lattices in a rotating dipolar Bose-Einstein condensate (BEC) with two- and three-body interactions. For this aim, we numerically solve the quasi two-dimensional, cubic-quintic Gross-Pitaevskii equation with nonlocal dipole-dipole nonlinearity. We find the critical rotation frequency for vortex formation in a pure dipolar BEC and also in a dipolar BEC with presence of both two- and three-body interactions. We also show the vortex lattices in a dipolar BEC with two- and three-body interactions for large rotation frequencies.
We investigate the vortex formation properties of a three-dimensional (3D) dipolar Bose-Einstein condensate (BEC) of 52 Cr atoms in an optical lattice potential through numerical simulations of the time-dependent Gross-Pitaevskii equation with a dissipation term. The mechanisms that influence the dipole-dipole interaction and the repulsive contact interaction between atoms during vortex formation are analyzed. We find that the stability of the vortices weakens with increasing attractive dipolar strength and that the repulsive contact interaction between atoms can increase the number of vortices.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.