Optimal generation of Fock states in a weakly nonlinear oscillator

We apply optimal control theory to determine the shortest time in which an energy eigenstate of a weakly anharmonic oscillator can be created under the practical constraint of linear driving. We show that the optimal pulses are beatings of mostly the transition frequencies for the transitions up to the desired state and the next leakage level. The time of a shortest possible pulse for a given nonlinearity scale with the nonlinearity parameter delta as a power law of alpha with alpha=-0.73 +/-0.029. This is a qualitative improvement relative to the value alpha=1 suggested by a simple Landau-Zener argument.