Analytic solution for strong-field quantum control of atomic wave packets

A simple analytic formula is derived for the impulse that will produce approximately, for arbitrarily large population transfer, a specified wave packet in a Rydberg atom. This solution to the nonlinear control problem is obtained in the limit that the duration of the pulsed control field is less than the Kepler period of the system. The validity of our solution is tested by comparison with a direct numerical integration of Schrodinger's equation, and it is found to yield the target state and population transfer with very high fidelity.