  In this paper, we discuss the compatibility between the rotating-wave and the
adiabatic approximations for controlled quantum systems. Although the paper
focuses on applications to two-level quantum systems, the main results apply in
higher dimension. Under some suitable hypotheses on the time scales, the two
approximations can be combined. As a natural consequence of this, it is
possible to design control laws achieving transitions of states between two
energy levels of the Hamiltonian that are robust with respect to
inhomogeneities of the amplitude of the control input.
