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Bichromatic control of dynamical tunneling: influence of the irregular Floquet states

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.