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arXiv:cond-mat/0103310 · Physical Review Letters

Creating Vortex Rings and Three-Dimensional Skyrmions in Bose-Einstein Condensates

Janne Ruostekoski, J. R. Anglin

Published Apr 30, 2001• 264 citations
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Abstract

We propose a method of generating a vortex ring in a Bose-Einstein condensate by means of electromagnetically induced atomic transitions. Some remnant population of atoms in a second internal state remains within the toroidal trap formed by the mean-field repulsion of the vortex ring. This population can be removed, or it can be made to flow around the torus (i.e., within the vortex ring). If this flow has a unit topological winding number, the entire structure formed by the two condensates is an example of a three-dimensional Skyrmion texture.

DOI
10.1103/physrevlett.86.3934

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We propose a method of generating a vortex ring in a Bose-Einstein condensate by means of electromagnetically induced atomic transitions. Some remnant population of atoms in a second internal state remains within the toroidal trap formed by the mean-field repulsion of the vortex ring. This population can be removed, or it can be made to flow around the torus (i.e., within the vortex ring). If this flow has a unit topological winding number, the entire structure formed by the two condensates is an example of a three-dimensional Skyrmion texture.
When an obstacle is moved in a superfluid faster than a critical velocity, quantized vortices are generated behind the obstacle. Here we propose a method to create more complicated topological excitations, three-dimensional skyrmions, behind a moving obstacle. We numerically show that, in a two-component Bose-Einstein condensate, component-dependent obstacle potentials can generate skyrmions in the wake, made up of quantized vortex rings in different components that are linked with each other. The lifetime of generated skyrmions can be prolonged by a guiding potential, which enables the formation of a skyrmion train.
We propose a new scheme for creating three-dimensional Skyrmions in a ferromagnetic spin-1 Bose-Einstein condensate by manipulating a multipole magnetic field and a pair of counter-propagating laser beams. The result shows that a three-dimensional Skyrmion with topological number Q = 2 can be created by a sextupole magnetic field and the laser beams. Meanwhile, the vortex ring and knot structure in the Skyrmion are found. The topological number can be calculated analytically in our model, which implies that the method can be extended to create Skyrmions with arbitrary topological number. As the examples, three-dimensional Skyrmions with Q = 3, 4 are also demonstrated and are distinguishable by the density distributions with a specific quantization axis. These topological objects have the potential to be realized in ferromagnetic spin-1 Bose-Einstein condensates experimentally.
Searching for novel topological objects is always an intriguing task for scientists in various fields. We study a three-dimensional (3D) topological structure called a 3D dimeron in trapped two-component Bose-Einstein condensates. The 3D dimeron differs from the conventional 3D skyrmion for the condensates hosting two interlocked vortex rings. We demonstrate that the vortex rings are connected by a singular string and the complexity constitutes a vortex molecule. The stability of the 3D dimeron is examined in two different models using the imaginary time evolution method. We find that the stable 3D dimeron can be naturally generated from a vortex-free Gaussian wave packet incorporating a synthetic non-Abelian gauge potential into the condensates.
The topological transition of vortex lines to vortex rings and hopfions is numerically investigated by the Gross–Pitaevskii equation in three-dimensional trapped Bose–Einstein condensates. The shape of the vortex rings formed by the two vortex lines of the vortex dipole depends strongly on the initial separation of the lines. An approximately perfect vortex ring can be obtained by choosing some suitable values of the separation. The deformation of the formed rings depends on the shape of the rings in turn. Furthermore, we show a feasible approach to generate vortex hopfions by imprinting a vortex line in the center of the generated vortex rings. Specifically, the movement of the vortex rings can excite helical waves along the central vortex line of the hopfion structure if the vortex ring is not perfect.
The three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive BECs subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold, and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamical evolutions under large atomic interaction strengths. The former exhibits simultaneously symmetrical splitting in the transverse plane, while the latter displays periodically expand-merge cycles in the longitudinal direction.
A three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive Bose-Einstein condensates subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamic evolutions under large atomic interaction strengths. The former exhibits simultaneous symmetric splitting in the transverse plane, while the latter displays periodic expand-merge cycles in the longitudinal direction.