Bose-Einstein condensates with vortices in rotating traps

TL;DR

This paper studies vortex solutions in rotating Bose-Einstein condensates, combining numerical algorithms, a variational Ansatz, and analytical methods to understand vortex stabilization, arrangement, and detection in both 2D and 3D configurations.

Contribution

It introduces a variational Ansatz for vortex energy in the Thomas-Fermi regime and provides analytical and numerical insights into vortex stabilization and detection methods.

Findings

Vortices are stabilized by trap rotation.

The variational Ansatz simplifies vortex energy calculations.

Analytical methods suggest detection via time-of-flight and interference.

Abstract

We investigate minimal energy solutions with vortices for an interacting Bose-Einstein condensate in a rotating trap. The atoms are strongly confined along the axis of rotation z, leading to an effective 2D situation in the x-y plane. We first use a simple numerical algorithm converging to local minima of energy. Inspired by the numerical results we present a variational Ansatz in the regime where the interaction energy per particle is stronger than the quantum of vibration in the harmonic trap in the x-y plane, the so-called Thomas-Fermi regime. This Ansatz allows an easy calculation of the energy of the vortices as function of the rotation frequency of the trap; it gives a physical understanding of the stabilisation of vortices by rotation of the trap and of the spatial arrangement of vortex cores. We also present analytical results concerning the possibility of detecting vortices by a time-of-flight measurement or by interference effects. In the final section we give numerical results for a 3D configuration.