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Strongly Rydberg-blockaded two-level atoms form a Rydberg superatom, which isexcited only to a collective symmetrical Dicke state. However, emerging oftenin the alkali-earth atoms, the spontaneous decay from the Rydberg state to anadditional pooling state renders the ensemble no longer a closed superatom.Herein we present a computationally-efficient model to characterize theinteraction between a fully Rydberg-blockaded ensemble of $N$ $\Lambda$-typethree-level atoms and a strong probe light field in a coherent state. The modelenables us to achieve a decomposition of the coupled dynamics in the strongfield limit, which significantly reduces the complexity of computing the$N$-body system evolution and paves a way for practical analysis inexperiments. A quasi-steady-state power spectrum with multiple sidebands isfound in the scattered field. The relative heights of the sidebands show a timedependence determined by the atomic relaxation, which illuminates potentialapplications of using the system in information transfer of quantum networks.With negligible dissipative flipping to the unsymmetrical states, the atomicrelaxation time indicating a linearly increasing pooling state fraction isderived analytically as a function of the atom number.

Spontaneous decay induced quantum dynamics in Rydberg blockaded {\Lambda}-type atoms