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arXiv:cond-mat/9911201 · Journal of Physics B Atomic Molecular and Optical Physics

Bose-Einstein condensation in a rotating anisotropic TOP trap

J. Arlt, Onofrio M. Maragò, E Hodby, S A Hopkins, G Hechenblaikner, S Webster, Christopher J. Foot

Published Dec 2, 1999• 18 citations
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Abstract

We describe the construction and operation of a time-orbiting potential trap that has different oscillation frequencies along its three principal axes. These axes can be rotated and we have observed Bose-Einstein condensates of 87 Rb with a rotating ellipsoidal shape. Under these conditions it has been predicted that quantized vortices form and are stable.

DOI
10.1088/0953-4075/32/24/320

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We describe the construction and operation of a time-orbiting potential trap that has different oscillation frequencies along its three principal axes. These axes can be rotated and we have observed Bose-Einstein condensates of 87 Rb with a rotating ellipsoidal shape. Under these conditions it has been predicted that quantized vortices form and are stable.
We present results on the size, density, chemical potential, and lifetime of a Bose-Einstein condensate as a function of the number of condensate atoms for parameters appropriate to the time-averaged orbiting potential trap in which a Bose condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms was recently formed [M. H. Anderson et al., Science 269, 198 (1995)]. These results were obtained by solving the time-independent nonlinear Schr\"odinger equation with anisotropic harmonic trapping potential. We also find vortex solutions for the trap and the critical rotation frequency required for their formation.
The behaviors of a rapidly rotating Bose-Einstein condensate under extreme elongation in a two-dimensional anisotropic harmonic plus quartic trap are investigated. Due to the quartic trap, the system remains stable at high rotating velocity, $\ensuremath{\Omega}\ensuremath{\geqslant}{\ensuremath{\omega}}_{\ensuremath{\perp}}$ (${\ensuremath{\omega}}_{\ensuremath{\perp}}$ is the radial harmonic trap frequency), and vortex lattices form even in the absence of the repulsive sss-wave interaction (ggg). When ggg is present, the interplay between ggg and the quartic trap potential can lead to rich vortex lattice transition states as a function of $\ensuremath{\Omega}$, to which vortex lattices vanish eventually at some higher $\ensuremath{\Omega}$.
The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.
We have studied the ground state configurations of a rotating Bose—Einstein condensation in a toroidal trap as the radius of the central Gaussian potential expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the gaussian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.
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.