Dynamics of Vortex Lattice Formation in a Rotating Bose-Einstein Condensate with an Optical Lattice Potential

We study dynamics of quantized vortex lattice formation in a rotating Bose-Einstein condensate with a square blue-detuned optical lattice by solving the Gross-Pitaevskii equation. This dynamics depends on the depth of the optical lattice. Vortices tend to form a triangular lattice under the rotation, while an optical lattice likes to pin vortices at their peaks. Such a competition of two effects makes this system more interesting and complicated.