  We present theoretical and experimental results on high-fidelity transfer of
a trapped Bose-Einstein condensate into its first vibrationally excited
eigenstate. The excitation is driven by mechanical motion of the trap, along a
trajectory obtained from optimal control theory. Excellent agreement between
theory and experiment is found over a large range of parameters. We develop an
approximate model to map the dynamics of the many-body condensate wave function
to a driven two-level system.
