  We investigate the quantum electrodynamics of a single two-level atom located
at the focus of a parabolic cavity. We first work out the modifications of the
spontaneous emission induced by the presence of this boundary in the optical
regime, where the dipole and the rotating-wave approximations apply.
Furthermore, the single-photon state that leaves the cavity asymptotically is
determined. The corresponding time-reversed single-photon quantum state is
capable of exciting the atom in this extreme multimode scenario with near-unit
probability. Using semiclassical methods, we derive a photon-path
representation for the relevant transition amplitudes and show that it
constitutes a satisfactory approximation for a wide range of wavelengths.
