Optimal Control of the Electronic Current Density - An application to one- and two-dimensional one-electron systems

TL;DR

This paper introduces a quantum optimal control approach using target functionals based on one-particle density and current, aiming to enhance stability of quantum states in one- and two-dimensional systems.

Contribution

It proposes a novel target functional formulation in quantum control that incorporates density and current, enabling the use of density-functional theory for system dynamics.

Findings

Optimized states show increased stability.

Functional successfully balances density overlap and current minimization.

Applicable to one- and two-dimensional one-electron systems.

Abstract

Quantum optimal control theory is a powerful tool for engineering quantum systems subject to external fields such as the ones created by intense lasers. The formulation relies on a suitable definition for a target functional, that translates the intended physical objective to a mathematical form. We propose the use of target functionals defined in terms of the one-particle density and its current. A strong motivation for this is the possibility of using time-dependent density-functional theory for the description of the system dynamics. We exemplify this idea by defining an objective functional that on one hand attempts a large overlap with a target density and on the other hand minimizes the current. The latter requirement leads to optimized states with increased stability, which we prove with a few examples of one- and two-dimensional one-electron systems.