Ground-state selection via many-body superradiant decay

For a single particle, relaxation into different ground states is governed by fixed branching ratios determined by the transition matrix element and the environment. Here, we show that in many-body open quantum systems the occupation probability of one ground state can be boosted well beyond what is dictated by single-particle branching ratios. Despite the competition, interactions suppress all but the dominant decay transition, leading to a 'winner takes all' dynamic where the system primarily settles into the dominant ground state. We prove that, in the presence of permutation symmetry, this problem is exactly solvable for any number of competing channels. Additionally, we develop an approximate model for the dynamics by mapping the evolution onto a fluid continuity equation, and analytically demonstrate that the dominant transition ratio converges to unity as a power law with increasing system size, for any branching ratios. This near-deterministic preparation of the dominant ground state has broad applicability. As an example, we discuss a protocol for molecular photoassociation where collective dynamics effectively acts as a catalyst, amplifying the yield in a specific final state. Our results open new avenues for many-body strategies in the preparation and control of quantum systems.