On the shape of vortices for a rotating Bose Einstein condensate

TL;DR

This paper analyzes how the shape of vortices in a rotating Bose-Einstein condensate depends on the trap's geometry and rotational velocity, revealing straight vortices in pancake-shaped condensates and bent vortices in cigar-shaped ones.

Contribution

It provides a theoretical analysis of vortex shapes in BECs based on simplified energy models, linking vortex geometry to trap anisotropy and rotation.

Findings

Vortices are straight in pancake-shaped condensates.

Vortices are bent in cigar-shaped condensates.

The vortex shape results from energy competition between length and rotation effects.

Abstract

For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived in Aftalion-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.