Scaling law for three-body collisions near a narrow s-wave Feshbach resonance

Ultracold atomic gases provide a controllable system to investigate the universal scaling laws of three-body physics, that is how the three-body recombination depends on the two-body scattering length. Although these scaling laws have been carefully examined in the bosonic systems, their manifestation in fermionic systems remain elusive. In this study, we investigate the three-body atomic loss rate L₃ in a two-component ⁶Li Fermi gas with a negative scattering length a < 0. Our experimental results indicate that the scaling law exists near the narrow s-wave Feshbach resonance, characterized by L₃ ∝ ∣a∣^2.60. This scaling is observed to be valid only within a certain range of a, breaking down at both extremes. On one end, in the unitary regime where ∣a∣ approaches infinity, the collisional rate becomes independent of a. On the other end, as a approaches zero, a change in the length scale occurs, resulting in L₃ ∝ r ^2.30_vdw , where the van der Waals length r_vdw becomes the dominate scaling length. This study resolves the puzzle of the scaling law on the Bardeen-Cooper-Schrieffer (BCS) side of a two-component Fermi gas, shedding light on the universal physics in few-body systems.