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arXiv:1011.2125 · Physical Review A

Structural change of vortex patterns in anisotropic Bose-Einstein condensates

Nicola Lo Gullo, Thomas Busch, Mauro Paternostro

Published May 10, 2011• 13 citations
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Abstract

We study the changes in the spatial distribution of vortices in a rotating Bose-Einstein condensate due to an increasing eccentricity of the trapping potential. By breaking the rotational symmetry, the vortex system undergoes a rich variety of structural changes, including the formation of zigzag and linear configurations. These spatial rearrangements are well signaled by the change in the behavior of the vortex-pattern eigenmodes against the eccentricity parameter. This behavior allows to actively control the distribution of vorticity in many-body systems and opens the possibility of studying interactions between quantum vortices over a large range of parameters.

DOI
10.1103/physreva.83.053612

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In this work, we study Bose–Einstein condensation in a system, where the rotation frequency decreases radially from the center. The system is described by a modified Gross–Pitaevskii equation that includes a nonuniform rotation term controlled by a parameter [Formula: see text], with the length scale of the rotation variation fixed relative to the healing length. The results show behavior distinctly different from the uniformly rotating condensate. In the uniform case, a triangular vortex lattice forms, whereas here we observe that above a critical value [Formula: see text] the vortices arrange themselves into a circular ring-shaped pattern near the boundary. Below [Formula: see text], the vortex configuration is disordered, lacking both triangular symmetry and a clear ring structure. The energy and chemical potential exhibit a sharp change at [Formula: see text], signaling a structural phase transition. A phase diagram is presented for the transition from the disordered to the ring-shaped vortex arrangement. The findings are discussed in the context of current experiments on synthetic gauge fields and structured rotation.
We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.
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.