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Physical Review A

Vortex stability near the surface of a Bose-Einstein condensate

Usama Al Khawaja

Published Dec 22, 2003• 2 citations
Publisher

Abstract

We investigate energetic stability of vortices near the surface of a Bose-Einstein condensate. From an energy functional of a rotating Bose-Einstein condensate, written in terms of variables local to the surface, and a suitable trial wave function, we calculate the energy of a moving vortex. The energetic stability of the vortex is investigated in terms of the rotation frequency of the confining potential. The critical frequency at which the vortices enter the condensate is calculated and compared with the experiment where a reasonable agreement is obtained.

DOI
10.1103/physreva.68.063614

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We investigate energetic stability of vortices near the surface of a Bose-Einstein condensate. From an energy functional of a rotating Bose-Einstein condensate, written in terms of variables local to the surface, and a suitable trial wave function, we calculate the energy of a moving vortex. The energetic stability of the vortex is investigated in terms of the rotation frequency of the confining potential. The critical frequency at which the vortices enter the condensate is calculated and compared with the experiment where a reasonable agreement is obtained.
We investigate energetic stability of vortices near the surface of a Bose-Einstein condensate. From an energy functional of a rotating Bose-Einstein condensate, written in terms of variables local to the surface, and a suitable trial wavefunction we calculate the energy of a moving vortex. The energetic stability of the vortex is investigated in terms of the rotation frequency of the confining potential. The critical frequency at which the vortices enter the condensate is calculated and compared with the experiment where a reasonable agreement is obtained.
We derive the frequency of precession and conditions for stability for a quantized vortex in a single-component and a two-component Bose-Einstein condensate. The frequency of precession is proportional to the gradient of the free energy with respect to displacement of the vortex core. In a two-component system, it is possible to achieve a local minimum in the free energy at the center of the trap. The presence of such a minimum implies the existence of a region of energetic stability where the vortex cannot escape and where one may be able to generate a persistent current.
Vortex states of weakly interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the Gross-Pitaevskii equation for the condensate in imaginary time. The total energies between states with and without a vortex are compared, yielding critical rotation frequencies that depend on the anisotropy of the trap and the number of atoms. Vortices displaced from the center of nonrotating traps are found to have long lifetimes for sufficiently large numbers of atoms. The relationship between vortex stability and bound core states is explored.
We consider the quantum reflection of vortices in Bose-Einstein condensates incident on a solid surface. Compared with the condensate without angular momentum, the rotation of the vortex gives unique opportunities to consider the interaction process between a matter wave and a solid surface. Due to the atom-surface interaction and dynamic excitations induced by interatomic interaction, our numerical simulations show that the reflected vortex would become unstable for sufficiently low velocity and large interaction strength. The stability diagram for the reflected vortex is given, and physical mechanism for this stability diagram is discussed. It is found that the expansion ratio between the reflected and incident vortices gives the boundary between stable and unstable regions for the reflected vortex.
For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived by Aftalion and Riviere [Phys. Rev. A 64, 043611 (2001)] in order to determine the shape of the vortex line according to the rotational velocity and the elongation of the condensate. The energy reflects the competition between the length of the vortex, which needs to be minimized taking into account the anisotropy of the trap, and the rotation term, which pushes the vortex along the z axis. We prove that if the condensate has the shape of a pancake, the vortex stays straight along the z axis, while in the case of a cigar, the vortex is bent. We study the local stability of the straight vortex and find an estimate for the critical angular speed at which bent vortices are nucleated. When vortices are nucleated, we prove that they must have some finite length.
The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmonic potential under forced rotation. By solving the non-linear Bogoliubov equations coupled with the Gross-Pitavskii equation, the elementary excitations and the total energy of the systems are calculated as a function of rotation velocity. There are two distinct criteria of vortex stability; The position of the excitation energy levels relative to the condensate energy level yields the local stability criterion, and the total energy relative to that of the non-vortex state yields the global stability criterion. The vortex stability phase diagram in the rotation velocity vs the particle density of the system is obtained, allowing one to locate the appropriate region to observe the singly quantized vortex.