  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.
