Time Dependence of Few-Body Forster Interactions Among Ultracold Rydberg Atoms

Rubidium Rydberg atoms in either |mj| sublevel of the 36p3/2 state can exchange energy via Stark-tuned Förster resonances, including two-, three-, and four-body dipole-dipole interactions. Three-body interactions of this type were first reported and categorized by Faoro et al. [Nat. Commun. 6, 8173 (2015)] and their Borromean nature was confirmed by Tretyakov et al. [Phys. Rev. Lett. 119, 173402 (2017)]. We report the time dependence of the N-body Förster resonance N×36p3/2,|mj|=1/2→36s1/2+37s1/2+(N−2)×36p3/2,|mj|=3/2, for N=2, 3, and 4, by measuring the fraction of initially excited atoms that end up in the 37s1/2 state as a function of time. The essential features of these interactions are captured in an analytical model that includes only the many-body matrix elements and neighboring atom distribution. A more sophisticated simulation reveals the importance of beyond-nearest-neighbor interactions and of always-resonant interactions.