  We investigate the quantum dynamics of a two-level system driven by a
bichromatic field, using a non-perturbative analysis. We make special emphasis
in the case of two large frequencies, where the Magnus expansion can fail, and
in the case of a large and a small frequency, where resonances can dominate. In
the first case, we show that two large frequencies can be combined to produce
an effective adiabatic evolution. In the second case, we show that high
frequency terms (which naturally arise as corrections to the adiabatic
evolution obtained in the first case) can be used to produce a highly tunable
adiabatic evolution over the whole Bloch sphere, controlled by multi-photon
resonances.
