  Resonance fluorescence in the Heitler regime provides access to single
photons with coherence well beyond the Fourier transform limit of the
transition, and holds the promise to circumvent environment-induced dephasing
common to all solid-state systems. Here we demonstrate that the coherently
generated single photons from a single self-assembled InAs quantum dot display
mutual coherence with the excitation laser on a timescale exceeding 3 seconds.
Exploiting this degree of mutual coherence we synthesize near-arbitrary
coherent photon waveforms by shaping the excitation laser field. In contrast to
post-emission filtering, our technique avoids both photon loss and degradation
of the single photon nature for all synthesized waveforms. By engineering
pulsed waveforms of single photons, we further demonstrate that separate
photons generated coherently by the same laser field are fundamentally
indistinguishable, lending themselves to creation of distant entanglement
through quantum interference.
