  We investigate the photon statistics of a single-photon source that operates
under non-stationary conditions. The photons are emitted by shining a periodic
sequence of laser pulses on single atoms falling randomly through a
high-finesse optical cavity. Strong antibunching is found in the intensity
correlation of the emitted light, demonstrating that a single atom emits
photons one-by-one. However, the number of atoms interacting with the cavity
follows a Poissonian statistics so that, on average, no sub-Poissonian photon
statistics is obtained, unless the measurement is conditioned on the presence
of single atoms.
