We investigate the dynamics of a generic interacting many-body system under
conditions of electromagnetically induced transparency (EIT). This problem is
of current relevance due to its connection to non-linear optical media realized
by Rydberg atoms. In an interacting system the structure of the dynamics and
the approach to the stationary state becomes far more complex than in the case
of conventional EIT. In particular, we discuss the emergence of a metastable
decoherence free subspace, whose dimension for a single Rydberg excitation
grows linearly in the number of atoms. On approach to stationarity this leads
to a slow dynamics which renders the typical assumption of fast relaxation
invalid. We derive analytically the effective non-equilibrium dynamics in the
decoherence free subspace which features coherent and dissipative two-body
interactions. We discuss the use of this scenario for the preparation of
collective entangled dark states and the realization of general unitary
dynamics within the spin-wave subspace.Comment: 13 pages, 3 figure