  Bichromatic control, in terms of the amplitude and relative phase of the
second field as control knobs, is an useful approach for controlling a variety
of quantum processes. In this context, understanding the features of the
control landscape is important to assess the extent and efficiency of the
control process. A key question is whether, for a given quantum process, one
can have regions wherein there is a complete lack of control. In this work we
show that such regions do exist and can be explained on the basis of the phase
space nature of the quantum Floquet states. Specifically, we show that robust
regions of no control arise due to the phenomenon of chaos-assisted tunneling.
We also comment on the possible influence of such regions on the phenomenon of
directed transport in quantum Hamiltonian ratchets.
