  The transversely confined propagating modes of an optical fiber mediate
virtually infinite range energy exchanges among atoms placed within their
field, which adds to the inherent free space dipole-dipole coupling. Typically,
the single atom free space decay rate largely surpasses the emission rate into
the guided fiber modes. However, scaling up the atom number as well as the
system size amounts to entering a collective emission regime, where
fiber-induced superradiant spontaneous emission dominates over free space
decay. We numerically study this super- and subradiant decay of highly excited
atomic states for one or several transverse fiber modes as present in hollow
core fibers. As particular excitation scenarios we compare the decay of a
totally inverted state to the case of Pi/2 pulses applied transversely or along
the fiber axis as in standard Ramsey or Rabi interferometry. While a mean field
approach fails to correctly describe the initiation of superradiance, a
second-order approximation accounting for pairwise atom-atom quantum
correlations generally proves sufficient to reliably describe superradiance of
ensembles from two to a few hundred particles. In contrast, a full account of
subradiance requires the inclusion of all higher order quantum correlations.
Considering multiple guided modes introduces a natural effective cut-off for
the interaction range emerging from the dephasing of different fiber
contributions.
