  We consider the phase stability of a local oscillator (or laser) locked to a
cavity QED system comprised of atoms with an ultra-narrow optical transition.
The atoms are cooled to millikelvin temperatures and then released into the
optical cavity. Although the atomic motion introduces Doppler broadening, the
standing wave nature of the cavity causes saturated absorption features to
appear, which are much narrower than the Doppler width. These features can be
used to achieve an extremely high degree of phase stabilization, competitive
with the current state-of-the-art. Furthermore, the inhomogeneity introduced by
finite atomic velocities can cause optical bistability to disappear, resulting
in no regions of dynamic instability and thus enabling a new regime accessible
to experiments where optimum stabilization may be achieved.
