Quantum optimal control within the rotating-wave approximation

We study the interplay between rotating-wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time independent under the rotating-wave approximation. Thus, we show how to recast the functional minimization defined by the optimal control problem into a simpler multivariable function minimization. We provide the analytic solution to the state-to-state transfer of the paradigmatic two-level system and to the more general star configuration of an N-level system. We demonstrate numerically the usefulness of this approach in the more general class of connected acyclic N-level systems with random spectra. Finally, we use it to design a protocol to entangle Rydberg via constant laser pulse atoms in an experimentally relevant range of parameters.