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Physical Review Letters

Nucleation and Growth of Vortices in a Rotating Bose-Einstein Condensate

Oleg Vorov, P. Van Isacker, Mahir Saleh Hussein, Klaus Bartschat

Published Dec 1, 2005• 14 citations
Publisher

Abstract

An analytic solution of the Gross-Pitaevskii equation for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The similarity of this behavior and mesoscopic superconductors is discussed.

DOI
10.1103/physrevlett.95.230406

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An analytic solution of the Gross-Pitaevskii equation for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The similarity of this behavior and mesoscopic superconductors is discussed.
We study the lowest energy states of a weakly interacting trapped atomic Bose-Einstein condensate in both quantum and classical cases. An analytic expression for the ground-state wavefunction of a rotating Gross-Pitaevskii condensate of trapped atoms describes the onset of vorticity in an accelerated trap, starting from the vortex entry followed by formation of growing symmetric Wigner molecules. Within a unified picture, it explains the staircase of the angular momentum jumps and the behavior of the bosonic occupancies observed in numerical and variational studies. The similarity of this behavior and mesoscopic superconductors is discussed.
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.
One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.
We study the dynamics of rotating two-component Bose-Einstein condensates(BECs) toward vortex lattice formation by numerically solving the two-dimensional Gross-Pitaevskii equations.The dynamics are similar to that of single-component BEC, and the whole changes of physical quantities in two cases are qualitatively similar.However, there are some differences between two cases.First, the characteristic time toward vortex entering depends on the inter-component interaction.The time toward vortex entering becomes shorter with increasing the inter-component interaction.Second, the angular momenta exchange between two components with keeping the total angular momentum.
Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. The log (base e) of total energy, trap energy, quantum energy, kinetic energy, internal energy and z-component of the angular momentum vs time were compared with f(x)=a+bx for that time when the vortices come in in the condensate. The increasing/decay rate of these energies and L_{z} were studied as a function of dissipation.
The dynamics and interaction of quantized vortices in Bose-Einstein condensates (BECs) are investigated by using the two-dimensional Gross-Pitaevskii equation (GPE) with/without an angular momentum rotation term. If all vortices have the same winding number, they would rotate around the trap center but never collide. In contrast, if the winding numbers are different, their interaction highly depends on the initial distance between vortex centers. The analytical results are presented to describe the dynamics of the vortex centers when β=0. While if β≠0, there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs. Finally, the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented.