Nonlinear dynamics for vortex lattice formation in a rotating Bose-Einstein condensate

TL;DR

This paper investigates how a rotating Bose-Einstein condensate responds to sudden rotation, revealing nonlinear dynamics that lead to vortex lattice formation through surface ripple excitations and instabilities.

Contribution

It introduces a detailed analysis of vortex nucleation mechanisms, combining dynamical and Landau instabilities, using the Gross-Pitaevskii equation and quasiparticle projection methods.

Findings

Quadrupole oscillations are excited by weak anisotropic rotation.

Surface mode populations exhibit recurrence oscillations that break down near resonance.

Vortices form from unstable surface ripples influenced by dissipation and instabilities.

Abstract

We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by the quasiparticle projection method. A simple recurrence oscillation of surface mode populations is broken in the quadrupole resonance region that depends on the trap anisotropy, causing stochastization of the dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.