  We study the dissipative propagation of quantized light in interacting
Rydberg media under the conditions of electromagnetically induced transparency
(EIT). Rydberg blockade physics in optically dense atomic media leads to strong
dissipative interactions between single photons. The regime of high incoming
photon flux constitutes a challenging many-body dissipative problem. We
experimentally study in detail for the first time the pulse shapes and the
second-order correlation function of the outgoing field and compare our data
with simulations based on two novel theoretical approaches well-suited to treat
this many-photon limit. At low incoming flux, we report good agreement between
both theories and the experiment. For higher input flux, the intensity of the
outgoing light is lower than that obtained from theoretical predictions. We
explain this discrepancy using a simple phenomenological model taking into
account pollutants, which are nearly-stationary Rydberg excitations coming from
the reabsorption of scattered probe photons. At high incoming photon rates, the
blockade physics results in unconventional shapes of measured correlation
functions.
