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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Vortex Lattices in Highly Anisotropic Traps

Suzanne McEndoo, Thomas Busch

Published Jun 1, 2007• 0 citations
Publisher

Abstract

Vortex lattices have become one of the most interesting areas of research in the area of cold atomic physics in recent years. When inducing a large amount of angular momentum into the ground state of a superfluid Bose-Einstein condensate, the sample responds by forming a so-called Abrikosov lattice. Within this lattice, vortices with winding number one are arranged in a triangular pattern that extends over the whole size of the sample. While the Abrikosov lattice is the exact solution for homogeneous condensates, it is also a very good solution for systems in isotropic harmonic traps. Due to the inhomogeneous potential however, the vortex lattice as a whole rotates within the trap.

DOI
10.1109/cleoe-iqec.2007.4386743

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Vortex lattices have become one of the most interesting areas of research in the area of cold atomic physics in recent years. When inducing a large amount of angular momentum into the ground state of a superfluid Bose-Einstein condensate, the sample responds by forming a so-called Abrikosov lattice. Within this lattice, vortices with winding number one are arranged in a triangular pattern that extends over the whole size of the sample. While the Abrikosov lattice is the exact solution for homogeneous condensates, it is also a very good solution for systems in isotropic harmonic traps. Due to the inhomogeneous potential however, the vortex lattice as a whole rotates within the trap.
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.
We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of a condensate in a anisotropic harmonic potential. The solution describes as limiting cases both a triangle vortex lattice in the symmetric potential trap and a quasi-one-dimensional structure of vortex rows in an asymmetric case, when the rotation frequency is very close to the lower trapping potential frequency. The shape of the density profile is found to be close to the Thomas-Fermi inverted paraboloid form, except in the vicinity of edges of a condensate cloud.
The fast rotation of a Bose Einstein condensate in a harmonic trap leads to a hexagonal lattice of vortices, called the Abrikosov lattice. Vortices are described as the zeros of the condensate wave function, which is a solution to a nonlinear Schrödinger equation type. We study the solutions of this equation on a specific eigenspace of the limiting problem, the Lowest Landau Level. Upper and lower bounds for the energy allow to determine the presence of a vortex lattice or the lack of visible vortices, as a function of the anisotropy and the rotation. The study of the critical regime is open and would need some numerical simulations. This constitutes a project in collaboration with Xavier Blanc and Nicolas Lerner.
We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensates in a rotating double-well trap potential and corotating optical lattice. We show that the vortex number does not diverge when the rotational frequency $\ensuremath{\Omega}\ensuremath{\rightarrow}1$ if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value l/l\sqrt{l}/ll​/l for l=4l=4l=4, which supports the conjecture that surface modes with angular momentum l=4l=4l=4 are excited when the rotating condensate is trapped in a double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning show very interesting features. We show the existence and pinning of hidden vortices whose phase profile is similar to that of the visible vortices.
We show that three-dimensional spherical-shell condensates respond to rotation by forming two aligned triangular Abrikosov-like vortex lattices on each hemispherical surface. The centrifugal force due to rotation causes an elliptical deformation of the spherical shell condensate shape and for faster rotation rates, drives the formation of a central multicharged vortex-antivortex pair at the poles surrounded by a ring of singly charged vortices in the bulk density. The vortex distributions observed in each hemisphere take a similar form to those found in rotating harmonic plus quartic traps.