Vortex-peak interaction and lattice shape in rotating two-component Bose-Einstein condensates

TL;DR

This paper analyzes how vortex lattice shapes in rotating two-component Bose-Einstein condensates depend on rotation and intercomponent interactions, deriving phase diagrams and critical velocities with theoretical and numerical validation.

Contribution

It introduces a point energy model to predict lattice shape transitions and provides formulas for vortex nucleation thresholds in complex geometries.

Findings

Lattice shape transitions from triangular to square are predicted by the model.

The phase diagram matches numerical simulations of Gross-Pitaevskii equations.

Critical velocities for vortex appearance are derived and validated.

Abstract

When a two-component Bose-Einstein condensate is placed into rotation, a lattice of vortices and cores appear. The geometry of this lattice (triangular or square) varies according to the rotational value and the intercomponent coupling strengths. In this paper, assuming a Thomas-Fermi regime, we derive a point energy which allows us to determine for which values of the parameters, the lattice goes from triangular to square. It turns out that the separating curve in the phase diagram agrees fully with the complete numerical simulations of the Gross-Pitaevskii equations. We also derive a formula for the critical velocity of appearance of the first vortex and prove that the first vortex always appears first in the component with largest support in the case of two disks, and give a criterion in the case of disk and annulus.