  The observation of quantum dot resonance fluorescence enabled a new
solid-state approach to generating single photons with a bandwidth almost as
narrow as the natural linewidth of a quantum dot transition. Here, we operate
in the Heitler regime of resonance fluorescence to generate sub-natural
linewidth and high-coherence quantum light from a single quantum dot. The
measured single-photon bandwidth exhibits a 30-fold reduction with respect to
the radiative linewidth of the QD transition and the single photons exhibit
coherence properties inherited from the excitation laser. In contrast,
intensity-correlation measurements reveal that this photon source maintains a
high degree of antibunching behaviour on the order of the transition lifetime
with vanishing two-photon scattering probability. This light source will find
immediate applications in quantum cryptography, measurement-based quantum
computing and, in particular, deterministic generation of high-fidelity
distributed entanglement among independent and even disparate quantum systems.
