Vortex patterns of a 2D rotating Bose-Einstein condensate at the critical rotational speed

TL;DR

This paper develops a GPU-accelerated variational method to study vortex patterns in 2D rotating Bose-Einstein condensates, revealing stable vortex arrays and collapse phenomena, and highlighting the analogy with superconducting vortices.

Contribution

It introduces a novel GPU-based computational framework with exact projection onto the Lowest Landau Level for analyzing vortex patterns in rotating BECs.

Findings

Reproduces Abrikosov vortex lattices with quantitative accuracy.

Identifies stable vortex arrays under weak attractive interactions.

Shows vortex collapse and radial contraction at strong attractions.

Abstract

We introduce a GPU-accelerated variational framework with exact projection onto the Lowest Landau Level to probe vortex patterns in rapidly rotating two-dimensional Bose-Einstein condensates. For repulsive interactions, our approach faithfully reproduces Abrikosov vortex lattices, achieving quantitative alignment with Thomas-Fermi theory and the Abrikosov constant, while underscoring the profound analogy between superfluid vortex ordering and Abrikosov lattices in type-II superconductors. In the attractive regime, we reveal that weak attractions sustain stable vortex arrays, whereas stronger attractions quench vortices, trigger radial contraction, and culminate in collapse at the Gagliardo-Nirenberg threshold. These findings deliver a cohesive numerical benchmark for vortex formation and collapse dynamics, forging a rigorous link between superfluidity and superconductivity in rotating quantum matter.