Coqblin-Schrieffer model for an ultracold gas of ytterbium atoms with metastable state

Abstract

Motivated by the impressive recent advance in manipulating cold ytterbium atoms we explore and substantiate the feasibility of realizing the Coqblin-Schrieffer model in a gas of cold fermionic $^{173}$Yb atoms. Making use of different AC polarizabillity of the electronic ground state (electronic configuration $^1S_0$) and the long lived metastable state (electronic configuration $^3P_0$), it is substantiated that the latter can be localized and serve as a magnetic impurity while the former remains itinerant. The exchange mechanism between the itinerant $^1S_0$ and the localized $^3P_0$ atoms is analyzed and shown to be antiferromagnetic. The ensuing SU(6) symmetric Coqblin-Schrieffer Hamiltonian is constructed, and, using the calculated exchange constant $J$, perturbative RG analysis yield the Kondo temperature $T_K$ that is experimentally accessible. A number of thermodynamic measurable observables are calculated in the weak coupling regime $T>T_K$ (using perturbative RG analysis) and in the strong coupling regime $T<T_K$ (employing known Bethe ansatz techniques).