  Single atoms or atom-like emitters are the purest source of on-demand single
photons, they are intrinsically incapable of multi-photon emission. To
demonstrate this degree of purity we have realized a tunable, on-demand source
of single photons using a single ion trapped at the common focus of high
numerical aperture lenses. Our trapped-ion source produces single-photon pulses
at a rate of 200 kHz with g$^2(0) = (1.9 \pm 0.2) \times 10^{-3}$, without any
background subtraction. The corresponding residual background is accounted for
exclusively by detector dark counts. We further characterize the performance of
our source by measuring the violation of a non-Gaussian state witness and show
that its output corresponds to ideal attenuated single photons. Combined with
current efforts to enhance collection efficiency from single emitters, our
results suggest that single trapped ions are not only ideal stationary qubits
for quantum information processing, but promising sources of light for scalable
optical quantum networks.
