Whereas in the familiar Kondo effect the exchange interaction is dipolar, it can also be multipolar, as has been realized in a recent experiment. Here we study multipolar Kondo effect in a Fermi gas of cold $^{ 173}$Yb atoms. Making use of different AC polarizability of the electronic ground state Yb($^{ 1}$S$_{ 0}$) and the long-lived metastable state Yb$^{ *}$($^{ 3}$P$_{ 2}$), it is suggested that the latter atoms can be localized and serve as a dilute concentration of magnetic impurities while the former ones remain itinerant. The exchange mechanism between the itinerant Yb and the localized Yb$^{ *}$ atoms is analyzed and shown to be antiferromagnetic. The quadruple and octuple interactions act to enhance the Kondo temperature $T_K$ that is found to be experimentally accessible. The bare exchange Hamiltonian needs to be decomposed into dipole ($d$), quadruple ($q$) and octuple ($o$) interactions in order to retain its form under renormalization group (RG) analysis, in which the corresponding exchange constants ($\lambda_{ \mathrm{ d}}$, $\lambda_{ \mathrm{ q}}$ and $\lambda_{ \mathrm{ o}}$) flow independently. Numerical solution of the RG scaling equations reveals a few finite fixed points, indicating an over-screening, which suggests a non-Fermi liquid phase. The impurity contribution to the magnetic susceptibility is calculated in the weak coupling regime (${ T}\gg{ T}_{ K}$).
Categories: cond-mat.quant-gas