Response of an atomic Bose-Einstein condensate to a rotating elliptical trap

We investigate numerically the response of an atomic Bose-Einstein condensate to a weakly-elliptical rotating trap over a large range of rotation frequencies. We analyse the quadrupolar shape oscillation excited by rotation, and discriminate between its stable and unstable regimes. In the latter case, where a vortex lattice forms, we compare with experimental observations and find good agreement. By examining the role of thermal atoms in the process, we infer that the process is temperature-independent, and show how terminating the rotation gives control over the number of vortices in the lattice. We also study the case of critical rotation at the trap frequency, and observe large centre-of-mass oscillations of the condensate.