  We realize a deterministic single-photon source from one and the same calcium
ion interacting with a high-finesse optical cavity. Photons are created in the
cavity with efficiency (88 +- 17)%, a tenfold improvement over previous
cavity-ion sources. Results of the second-order correlation function are
presented, demonstrating a high suppression of two-photon events limited only
by background counts. The cavity photon pulse shape is obtained, with good
agreement between experiment and simulation. Moreover, theoretical analysis of
the temporal evolution of the atomic populations provides relevant information
about the dynamics of the process and opens the way to future investigations of
a coherent atom-photon interface.
