  Within the framework of exact quantum electrodynamics in dispersing and
absorbing media, we have studied the quantum state of the radiation emitted
from an initially in the upper state prepared two-level atom in a high-$Q$
cavity, including the regime where the emitted photon belongs to a wave packet
that simultaneously covers the areas inside and outside the cavity. For both
continuing atom--field interaction and short-term atom--field interaction, we
have determined the spatio-temporal shape of the excited outgoing wave packet
and calculated the efficiency of the wave packet to carry a one-photon Fock
state. Furthermore, we have made contact with quantum noise theories where the
intracavity field and the field outside the cavity are regarded as
approximately representing independent degrees of freedom such that two
separate Hilbert spaces can be introduced.
