A Model for Overscreened Kondo Effect in Ultracold Fermi Gas

The feasibility of realizing overscreened Kondo effect in ultra-cold Fermi gas of atoms with spin $s \ge \tfrac{3}{2}$ in the presence of a localized magnetic impurity atom is proved realistic. Specifying to a system of ultra cold $^{22}$Na Fermi gas and a trapped $^{197}$Au impurity, the mechanism of exchange interaction between the Na and Au atoms is elucidated and the exchange constant is found to be antiferromagnetic. The corresponding exchange Hamiltonian is derived, and the Kondo temperature is estimated at the order of $1 \mu$K. Within a weak-coupling renormalization group scheme, it is shown that the coupling renormalizes to the non-Fermi liquid fixed point.