Vortex formation of a Bose-Einstein condensate in a rotating deep optical lattice

We study the dynamics of vortex nucleation and lattice formation in a Bose–Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross–Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by Williams {\it et al.} [Phys. Rev. Lett. {\bf 104}, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.