Observation of Universal Efimov's Ratios across an Intermediate-Strength Feshbach Resonance in 39 K

Efimov's original scenario is featured by an infinite number of three-body bound states (trimers) accumulating at unitarity where E = 1 / a = 0 . The binding energies of these trimers have a self-similar structure with a fixed scaling factor between adjacent branches. This scheme is valid in the zero-range limit and in real systems only applies to highly-excited trimers with finite-range interactions. In this work, we unambiguously measured the benchmarks associated with the Efimov spectrum in ³⁹ K , denoted as a_-⁽n = 0) , a_*⁽n = 1) and a₊⁽n = 0) , with n indexing the parentage of trimer. a_-⁽n) are tri-atomic resonances at a < 0 , a_*⁽n) are scattering resonances between atoms and Feshbach molecules at a > 0 , a₊⁽n) are interference minima in three-atom recombination at a > 0 . We report a universal ratio a_*⁽1) /a_-⁽0) on the two lowest-lying trimers. The within-ten-percent consistency between this ratio and zero-range result implies that finite range perturbations are suppressed as expected for Feshbach resonances with intermediate strength. We introduce multi-channel van der Waals three-body model that can reproduce all three benchmarks.