  We investigate the Rabi oscillation of an atom placed inside a quantum cavity
where each mirror is formed by a chain of atoms trapped near a one-dimensional
waveguide. This proposal was studied previously with the use of Markov
approximation, where the delay due to the finite travel time of light between
the two cavity mirrors is neglected. We show that Rabi oscillation analogous to
that obtained with high-finesse classical cavities is achieved only when this
travel time is much larger than the time scale that characterizes the
collective response of the atomic chain. Therefore, the delay must be taken
into account and the dynamics of the problem is inherently non-Markovian.
Parameters of interest such as the Rabi frequency and the cavity loss rate due
to photon leakage through the mirrors are obtained.
