  We show how the optical properties of a single semiconductor quantum dot can
be controlled with a small dc voltage applied to a gate electrode. We find that
the transmission spectrum of the neutral exciton exhibits two narrow lines with
$\sim 2$ $\mu$eV linewidth. The splitting into two linearly polarized
components arises through an exchange interaction within the exciton. The
exchange interaction can be turned off by choosing a gate voltage where the dot
is occupied with an additional electron. Saturation spectroscopy demonstrates
that the neutral exciton behaves as a two-level system. Our experiments show
that the remaining problem for manipulating excitonic quantum states in this
system is spectral fluctuation on a $\mu$eV energy scale.
