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

Ultracold atomic gases provide a controllable system to study the inelastic processes for three-body systems, where the three-body recombination rate depends on the scattering length scaling. Such scalings have been confirmed in bosonic systems with various interaction strengths, but their existence with fermionic atoms remains elusive. In this work, we report on an experimental investigation of the scaling law for the three-body atomic loss rate $L_3$ in a two-component $^6$Li Fermi gas with the scattering length $a<0$. The scaling law is validated within a certain range of $a$ near the narrow $s$-wave Feshbach resonance, where $L_3\propto T|a|^{2.60(5)}$, and $T$ is the gas temperature. The scaling law is observed to have an upper and a lower bound in terms of the scattering length. For the upper bound, when $a\rightarrow \infty$, the power-law scaling is suppressed by the unitary behavior of the resonance caused by the strong three-body collisions. For the lower bound, $a\rightarrow 0$, the finite range effect modifies the scaling law by the effective scattering length $L_e$. These results indicate that the three-body recombination rate in a fermionic system could be characterized by the scaling law associated with the generalized Efimov physics.