  A semiconductor quantum dot mimics a two-level atom. Performance as a single
photon source is limited by decoherence and dephasing of the optical
transition. Even with high quality material at low temperature, the optical
linewidths are a factor of two larger than the transform-limit. A major
contributor to the inhomogeneous linewdith is the nuclear spin noise. We show
here that the nuclear spin noise depends on optical excitation, increasing
(decreasing) with increasing resonant laser power for the neutral (charged)
exciton. Based on this observation, we discover regimes where we demonstrate
transform-limited linewidths on both neutral and charged excitons even when the
measurement is performed very slowly.
