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Dynamical tunneling and control

This article summarizes the recent work on the influence of dynamical tunneling on the control of quantum systems. Specifically, two examples are discussed. In the first, it is shown that the bichromatic control of tunneling in a driven double well system is hampered by the phenomenon of chaos-assisted tunneling. The bichromatic control landscape exhibits several regions indicating lack of control with every such region involving chaos-assisted tunneling. The second example illustrates the failure of controlling the dissociation dynamics of a driven Morse oscillator due to the phenomenon of resonance-assisted tunneling. In particular, attempts to control the dissociation dynamics by rebuilding local phase space barriers are foiled due to resonance-assisted tunneling.