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

TL;DR

The paper develops a GPU-accelerated variational framework with exact projection onto the Lowest Landau Level to study vortex patterns in rapidly rotating two-dimensional Bose–Einstein condensates. In the repulsive regime, it reproduces Abrikosov vortex lattices and TF-like density profiles, establishing a close link between superfluid vortex ordering and Abrikosov lattices in type-II superconductors. In the attractive regime, it reveals universal collapse scaling governed by the Gagliardo–Nirenberg threshold, with vortex structure diminishing as the condensate contracts toward collapse; this is validated by comparisons to GN theory and experiments. Together, the work provides a rigorous numerical benchmark bridging mean-field BEC vortex physics and superconductivity concepts, while offering a platform for extensions to finite temperature, three dimensions, and beyond-mean-field regimes.

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.

Figures (11)

• Figure 1: Density and phase of the condensate wave function $|\psi_\Omega|^2$ for $G=200$ in the weak effective trap $V^{\rm eff}_\Omega$ [see \ref{['eq:Veff']}]. Results are shown for rotation frequencies $\Omega=0.95$ and $\Omega=0.99$.
• Figure 2: Density of the condensate wave function $|\psi_G|^2$ for repulsive interactions in the weak effective trap $V^{\rm eff}_{\Omega=0.99}$ [see \ref{['eq:Veff']}]. The vortex pattern and corresponding energy distributions are shown for interaction strengths $G=50$ and $G=100$.
• Figure 3: Determine the theoretical energy density $e^{\rm Ab}(1)$ with $G=200$ in different $\Omega$ rotation levels in LLL space via the numerical mean-field, with the weak interaction potential $V^{\rm eff}_{\Omega}$ in \ref{['eq:Veff']}.
• Figure 4: Theoretical (red) and numerical (blue) density for mean-field approximation distribution, with $G = 200$ (repulsive interaction), for $\Omega = 0.95, 0.99$.
• Figure 5: Density and phase profiles of the condensate with attractive interactions at $\Omega=0.9$ for different $G$, obtained after $10^4$ imaginary-time steps and $2\times10^3$ real-time steps toward the energy-optimal ground state.