Controllability of wavepacket dynamics in coherently driven double-well potential

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 Gaussian wavepacket shows coherent oscillation between the wells. It is found that as there is an increase in strength and/or the number of frequency components of perturbation, the coherent motion of the Gaussian wavepacket changes to an irregular one with irreversible delocalization. We investigate the controllability of the system depending on the perturbation parameters and the initial quantum state by focusing mainly on the delocalized state generated by the polychromatical perturbation. 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 short-time control we show the difficulty of the control for the delocalized state because of the numerous local minima. Furthermore, it is demonstrated that the short-time control of the delocalized state can be assisted by chaotic behavior in the controlled-system with the polychromatic perturbation.