Time dependence of few-body Förster interactions among ultracold Rydberg atoms

Rubidium Rydberg atoms in either |m_j|-sublevel of the 36p_3/2 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 Ntimes 36p_3/2,|mj|=1/2→ 36s_1/2+37s_1/2+(N-2)times 36p_3/2,|mj|=3/2, for N=2,3, and 4, by measuring the fraction of initially excited atoms that end up in the 37s_1/2 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.