On the optimality of optical pumping for a closed $\Lambda$-system with large decay rates of the intermediate excited state

TL;DR

This paper demonstrates through optimal control theory that optical pumping is the optimal method for population transfer in a closed Lambda-system with large decay rates, confirmed by numerical simulations.

Contribution

It introduces a novel approach combining adiabatic elimination, basis transformation, and optimal control to establish optical pumping as optimal in such systems.

Findings

Optical pumping is optimal for population transfer in the specified Lambda-system.

The optimality holds even when decay rates vary significantly.

Numerical results confirm the theoretical predictions.

Abstract

We use optimal control theory to show that for a closed $\Lambda$-system where the excited intermediate level decays to the lower levels with a common large rate, the optimal scheme for population transfer between the lower levels is actually optical pumping. In order to obtain this result we exploit the large decay rate to eliminate adiabatically the weakly coupled excited state, then perform a transformation to the basis comprised of the dark and bright states, and finally apply optimal control to this transformed system. Subsequently, we confirm the optimality of the optical pumping scheme for the original closed $\Lambda$-system using numerical optimal control. We also demonstrate numerically that optical pumping remains optimal when the decay rate to the target state is larger than that to the initial state or the two rates are not very different from each other. The present work is expected to find application in various tasks of quantum information processing, where such systems are encountered.