  We numerically study the controllability of quantum dynamics in perturbed
one-dimensional double-well potential by using an optimal control theory. As
the perturbation strength is small the dynamics of the initially localized
aussian wavepacket in the right well shows coherent oscillation between the
wells like a behavior of instanton. It was found that as the increase of the
strength and/or the number of frequency components of the perturbation the
coherent motion changes the irregular one with irreversible delocalization of
the wavepacket. We investigate the controllability of the system depending on
the perturbation parameters and the initial state by focusing mainly on the
delocalized state generated in the polychromatically perturbed system. In the
relatively long-time control for the Gaussian wavepacket and the delocalized
state, we show that it is well-controllable via the first excited state doublet
in spite of the perturbation parameters. On the other hand, in the relatively
shor-time control we show the difficulty of the control for the delocalized
state because of the numerous local minima. Furthermore, it is demonstrated
that chaotic phase space structure of the system assists the controllability of
the delocalized state.
