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 the shortest possible pulse for a given nonlinearity scales with the nonlinearity parameter δ as a power law δ-α with α≅0.73±0.029. This is a qualitative improvement relative to the value α=1 suggested by a simple Landau-Zener argument.