Collective transition quenching in the presence of multiple competing decay channels

We present a theoretical framework for what we term as 'collective transition quenching', a many-body dissipative phenomenon that occurs in systems with multiple competing decay channels. Despite the competition, interactions suppress all but the dominant decay transition, leading to a 'winner takes all' dynamic where the ensemble primarily settles into the dominant ground state. We analytically show that the dominant transition ratio exhibits a power-law convergence to unity with increasing system size for any branching ratio. This allows for a near-deterministic preparation of the dominant ground state, with a massive speedup arising from Dicke superradiance. Our findings provide a concrete understanding of collective transition quenching, paving the way for efficient schemes for the generation and ground-state cooling of molecules and the preparation of entangled dark states.