  We experimentally observed an accumulative type of nonlinear attenuation and
distortion of slow light, i.e., Rydberg polaritons, with the Rydberg state
$|32D_{5/2}\rangle$ in the weak-interaction regime. The present effect of
attenuation and distortion cannot be explained by considering only the
dipole-dipole interaction (DDI) between Rydberg atoms in $|32D_{5/2}\rangle$.
Our observation can be attributed to the atoms in the dark Rydberg states other
than those in the bright Rydberg state, i.e., $|32D_{5/2}\rangle$, driven by
the coupling field. The dark Rydberg states are all the possible states, in
which the population decaying from $|32D_{5/2}\rangle$ accumulated over time,
and they were not driven by the coupling field. Consequently, the DDI between
the dark and bright Rydberg atoms increased the decoherence rate of the Rydberg
polaritons. We performed three different experiments to verify the above
hypothesis, to confirm the existence of the dark Rydberg states, and to measure
the decay rate from the bright to dark Rydberg states. In the theoretical
model, we included the decay process from the bright to dark Rydberg states and
the DDI effect induced by both the bright and dark Rydberg atoms. All the
experimental data of slow light taken at various probe Rabi frequencies were in
good agreement with the theoretical predictions based on the model. This study
pointed out an additional decoherence rate in the Rydberg-EIT effect, and
provides a better understanding of the Rydberg-polariton system.
