  We report results important for the creation of a best-of-both-worlds quantum
hybrid system consisting of a solid-state source of single photons and an
atomic ensemble as quantum memory. We generate single photons from a GaAs
quantum dot (QD) frequency-matched to the Rb D2-transitions and then use the Rb
transitions to analyze spectrally the quantum dot photons. We demonstrate
lifetime-limited QD linewidths (1.48 GHz) with both resonant and non-resonant
excitation. The QD resonance fluorescence in the low power regime is dominated
by Rayleigh scattering, a route to match quantum dot and Rb atom linewidths and
to shape the temporal wave packet of the QD photons. Noise in the solid-state
environment is relatively benign: there is a blinking of the resonance
fluorescence at MHz rates but negligible upper state dephasing of the QD
transition. We therefore establish a close-to-ideal solid-state source of
single photons at a key wavelength for quantum technologies.
