Three-body physics of Rydberg polaritons

Under the conditions electromagnetically induced transparency in Rydberg media, slow-light polaritons interact strongly via Rydberg states. While two such polaritons can interact attractively and form two-body bound states, three polariton physics remains largely unexplored. We show that while exact three-polariton bound states do not exist, metastable ones do. The understanding of three-polariton physics will allow for the construction of more precise low energy many-body theories of Rydberg polaritons and may enable the realization of novel exotic equilibrium and out-of equilibrium phenomena with interacting light.