Maximum population transfer in a periodically driven quantum system

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate-frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well-defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multilevel systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model.