Role of excited states in the splitting of a trapped interacting Bose-Einstein condensate by a time-dependent barrier

An essentially exact approach to compute the wave function in the time-dependent many-boson Schr?dinger equation is derived and employed to study accurately the process of splitting a trapped condensate. As the trap transforms from a single to double well the ground state changes from a coherent to a fragmented state. We follow the role played by many-body excited states during the splitting process. Among others, a "counterintuitive" regime is found in which the evolution of the condensate when the splitting is sufficiently slow is not to the fragmented ground state, but to a low-lying excited state which is a coherent state. Experimental implications are discussed.