  One of the key challenges in developing quantum networks is to generate
single photons with high brightness, purity, and long temporal coherence.
Semiconductor quantum dots potentially satisfy these requirements; however, due
to imperfections in the surrounding material, the coherence generally degrades
with increasing excitation power yielding a broader emission spectrum. Here we
overcome this power broadening regime and demonstrate the longest coherence at
exciton saturation where the detection count rates are highest. We detect
single-photon count rates of 460,000 counts per second under pulsed laser
excitation while maintaining a single-photon purity of greater than 99%.
Importantly, the enhanced coherence is attained with quantum dots in ultraclean
wurtzite InP nanowires, where the surrounding charge traps are filled by
exciting above the wurtzite InP nanowire bandgap. By raising the excitation
intensity, the number of possible charge configurations in the quantum dot
environment is reduced, resulting in a narrower emission spectrum. Via Monte
Carlo simulations we explain the observed narrowing of the emission spectrum
with increasing power. Cooling down the sample to 300 mK, we further enhance
the single-photon coherence two-fold as compared to operation at 4.5 K,
resulting in a homogeneous coherence time, T2, of 1.2 ns.
