  We study the dynamics of a single excitation coherently shared amongst an
ensemble of atoms and coupled to a one-dimensional wave guide. The coupling
between the matter and the light field gives rise to collective phenomena such
as superradiant states with an enhanced initial decay rate, but also to the
coherent exchange of the excitation between the atoms. We find that the
competition between the two phenomena provides a characteristic dynamics for
the decay of the excitations, and remarkably exhibits an algebraic behavior,
instead of the expected standard exponential one, for a large number of atoms.
The analysis is first performed for a chiral waveguide, where the problem can
be solved analytically, and then is extended to the bidirectional waveguide.
