  Strongly Rydberg-blockaded two-level atoms form a Rydberg superatom, which is
excited only to a collective symmetrical Dicke state. However, emerging often
in the alkali-earth atoms, the spontaneous decay from the Rydberg state to an
additional pooling state renders the ensemble no longer a closed superatom.
Herein we present a computationally-efficient model to characterize the
interaction between a fully Rydberg-blockaded ensemble of $N$ $\Lambda$-type
three-level atoms and a strong probe light field in a coherent state. The model
enables us to achieve a decomposition of the coupled dynamics in the strong
field limit, which significantly reduces the complexity of computing the
$N$-body system evolution and paves a way for practical analysis in
experiments. A quasi-steady-state power spectrum with multiple sidebands is
found in the scattered field. The relative heights of the sidebands show a time
dependence determined by the atomic relaxation, which illuminates potential
applications of using the system in information transfer of quantum networks.
With negligible dissipative flipping to the unsymmetrical states, the atomic
relaxation time indicating a linearly increasing pooling state fraction is
derived analytically as a function of the atom number.
