Multipolar Kondo Effect in ${}^1$S${}_0$-${}^3$P${}_2$ Mixture of ${}^{173}$Yb Atoms

Abstract

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${}^{\ast }$(${}^3$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${}^{\ast }$ 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 ($T\gg T_K$).

31 pages, 14 figures

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• Laser Manipulation of Spin-Exchange Interaction Between Alkaline-Earth Atoms in ${}^1$S${}_0$ and ${}^3$P${}_2$ States