  We propose a single-atom, cavity quantum electrodynamics system, compatible
with recently demonstrated, fiber-integrated micro- and nano-cavity setups, for
the on-demand production of optical number-state, $0N$-state, and
binomial-code-state pulses. The scheme makes use of Raman transitions within an
entire atomic ground-state hyperfine level and operates with laser and cavity
fields detuned from the atomic transition by much more than the excited-state
hyperfine splitting. This enables reduction of the dynamics to that of a
simple, cavity-damped Tavis-Cummings model with the collective spin determined
by the total angular momentum of the ground hyperfine level.
