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

We study the response of a trapped Bose-Einstein condensate to a sudden turn on of a rotating drive by numerically solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by a quasiparticle projection method. In a quadrupolar resonant regime, which depends on the trap anisotropy, simple periodic oscillations in surface-mode populations disappear and the system exhibits stochastic 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.