Controllability of Wavepacket Dynamics in Coherently Driven Double-Well Potential

TL;DR

This study investigates the controllability of quantum wavepacket dynamics in a perturbed double-well potential using optimal control theory, revealing how perturbation strength and phase space structure influence control effectiveness.

Contribution

It demonstrates the controllability of delocalized quantum states in a perturbed double-well system and highlights the role of phase space chaos in aiding control.

Findings

Long-time control is effective via the first excited state doublet.

Short-time control of delocalized states is hindered by local minima.

Chaotic phase space structures facilitate controllability.

Abstract

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.