Vortex patterns and sheets in segregated two component Bose-Einstein condensates

TL;DR

This paper analyzes vortex patterns in rotating two-component Bose-Einstein condensates, showing how interfaces evolve into vortex sheets as rotation increases, with energy estimates and interface behavior in the Thomas-Fermi regime.

Contribution

It provides new energy estimates and insights into interface behavior and vortex sheet formation in segregated two-component Bose-Einstein condensates under rotation.

Findings

Interface length increases with rotation, indicating vortex sheet formation.

New error estimates for Modica-Mortola type energies away from interfaces.

Energy decomposes into perimeter and rotational terms, guiding vortex pattern analysis.

Abstract

We study minimizers of a Gross-Pitaevskii energy describing a two-component Bose-Einstein condensate set into rotation. We consider the case of segregation of the components in the Thomas-Fermi regime, where a small parameter $\epsilon$ conveys a singular perturbation. We estimate the energy as a term due to a perimeter minimization and a term due to rotation. In particular, we prove a new estimate concerning the error of a Modica Mortola type energy away from the interface. For large rotations, we show that the interface between the components gets long, which is a first indication towards vortex sheets.