Vortex formation in a rotating reference frame

We create vortices in a trapped Bose-Einstein condensate by cooling the atomic sample through the phase transition in the presence of a rotating magnetic trapping potential. The thermal cloud remains in quasi-equilibrium during the cooling, ultimately producing condensates in the rotating ground state. We show that the trap rotation frequency at which a vortex first appears agrees closely with theoretical predictions. The number of vortices within the condensate is established by the rotation frequency at the phase transition; once the condensate has started to form, its vortex content is robust against frequency changes. Images of the condensate taken during evaporation suggest that the vortex spatial configuration is similarly determined early on in the growth of the condensate.