Quantum control of Rydberg wave packets in the strong-response regime

In this article, we describe an analytic approach to the quantum control of wave-packet dynamics. In particular, we show that the held that will produce a specified wave packet in a Rydberg atom can he found approximately from a simple analytic formula. This analytic solution is shown to hold even in the regime of strong excitation. and is found by limiting the duration of the pulsed control field to less than one Kepler period of the system. Comparison with a direct numerical integration of Schrodinger's equation shows that our solution yields the target state and population transfer with very high fidelity. The possibility of ionization to the continuum is also included in the model. The solution provides some insight into the multiplicity of solutions to the control problem and the relative complexity of the control-field shapes in the weak- and strong-response regimes.