Instabilities leading to vortex lattice formation in rotating Bose-Einstein condensates

We present a comprehensive theoretical study of vortex lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap. We consider rotating solutions of the classical hydrodynamic equations, their response to perturbations, as well as time-dependent simulations. We discriminate three distinct, experimentally testable, regimes of instability: {\em ripple}, {\em interbranch}, and {\em catastrophic}. Under symmetry-breaking perturbations these instabilities lead to lattice formation even at zero temperature. While our results are consistent with previous theoretical and experimental results, they shed new light on lattice formation.