  Each natural mode of the electromagnetic field within a parabolic mirror
exhibits spatial localization and polarization properties that can be exploited
for the quantum control of its interaction with atomic systems. The region of
localization is not restricted to the focus of the mirror leading to a
selective response of atomic systems trapped on its vicinity. We report
calculations of the spontaneous emission rates for an atom trapped inside the
mirror accounting for all atomic polarizations and diverse trapping regions. It
is shown that electric dipole transitions can be enhanced near the focus of a
deep parabolic mirror with a clear identification of the few vectorial modes
involved. Out of the focus the enhancement vanishes gradually, but the number
of relevant modes remains small. Ultimately this represents a quantum
electrodynamic system where internal and external degrees of freedom cooperate
to maximize a selective exchange and detection of single excitations.
