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arXiv:1512.00978 · Physical review. B./Physical review. B

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

Igor Kuzmenko, Tetyana Kuzmenko, Y. Avishai, Gyu-Boong Jo

Published Mar 29, 2016• 22 citations
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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 $^{173}\mathrm{Yb}$ atoms. Making use of different AC polarizabillity of the electronic ground state (electronic configuration $^{1}\mathrm{S}_{0}$) and the long lived metastable state (electronic configuration $^{3}\mathrm{P}_{0}$), 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 $^{1}\mathrm{S}_{0}$ and the localized $^{3}\mathrm{P}_{0}$ 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 renormalization group (RG) analysis yields 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).

DOI
10.1103/physrevb.93.115143

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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 173Yb^{173}\mathrm{Yb}173Yb atoms. Making use of different AC polarizabillity of the electronic ground state (electronic configuration 1S0^{1}\mathrm{S}_{0}1S0​) and the long lived metastable state (electronic configuration 3P0^{3}\mathrm{P}_{0}3P0​), 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 1S0^{1}\mathrm{S}_{0}1S0​ and the localized 3P0^{3}\mathrm{P}_{0}3P0​ atoms is analyzed and shown to be antiferromagnetic. The ensuing SU(6) symmetric Coqblin-Schrieffer Hamiltonian is constructed, and, using the calculated exchange constant JJJ, perturbative renormalization group (RG) analysis yields the Kondo temperature TK{T}_{K}TK​ that is experimentally accessible. A number of thermodynamic measurable observables are calculated in the weak-coupling regime T>TKT>{T}_{K}T>TK​ (using perturbative RG analysis) and in the strong-coupling regime T<TKT<{T}_{K}T<TK​ (employing known Bethe ansatz techniques).
Multipolar Kondo Effect in a 173^{173}173Yb(1^11S0_00​) - 173^{173}173Yb(3^33P2_22​) Mixture
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^{173}173Yb atoms. Making use of different AC polarizability of the electronic ground state Yb(1^{1}1S0_{0}0​) and the long-lived metastable state Yb∗^{*}∗(3^{3}3P2_{2}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 TKT_KTK​ that is found to be experimentally accessible. The bare exchange Hamiltonian needs to be decomposed into dipole (ddd), quadruple (qqq) and octuple (ooo) interactions in order to retain its form under renormalization group (RG) analysis, in which the corresponding exchange constants (λd\lambda_{\mathrm{d}}λd​, λq\lambda_{\mathrm{q}}λq​ and λo\lambda_{\mathrm{o}}λo​) 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≫TK{T}\gg{T}_{K}T≫TK​).
Whereas in the familiar Kondo effect the exchange interaction is dipolar, there are systems in which the exchange interaction is multipolar, as has been realized in a recent experiment. Here, we study multipolar Kondo effect in a Fermi gas of cold 173Yb^{173}\mathrm{Yb}173Yb atoms. Making use of different ac polarizabilities of the electronic ground state Yb(1S0)\mathrm{Yb}(^{1}\mathrm{S}_{0})Yb(1S0​) and the long-lived metastable state Yb∗(3P2){\mathrm{Yb}}^{*}(^{3}\mathrm{P}_{2})Yb∗(3P2​), 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∗{\mathrm{Yb}}^{*}Yb∗ atoms is analyzed and shown to be antiferromagnetic. The quadrupole and octupole interactions act to enhance the Kondo temperature TK{T}_{K}TK​ that is found to be experimentally accessible. The bare exchange Hamiltonian needs to be decomposed into dipole (d)(\text{d})(d), quadrupole (q)(\text{q})(q), and octupole (o)(\text{o})(o) interactions in order to retain its form under renormalization group (RG) analysis, in which the corresponding exchange constants $({\ensuremath{\lambda}}_{\text{d}},{\ensuremath{\lambda}}_{\text{q}}$, and ${\ensuremath{\lambda}}_{\text{o}})$ flow independently. Numerical solution of the RG scaling equations reveals a few finite fixed points. Arguments are presented that the Fermi-liquid fixed point at low temperature is unstable, indicating that the impurity is overscreened, which suggests a non-Fermi-liquid phase. The impurity contributions to the specific heat, entropy, and the magnetic susceptibility are calculated in the weak coupling regime $(T\ensuremath{\gg}{T}_{K})$, and are compared with the analogous results obtained for the standard case of dipolar exchange interaction (the $s\ensuremath{-}d$ Hamiltonian).
The feasibility of realizing the overscreened Kondo effect in ultracold Fermi gas of atoms with spin $s\ensuremath{\ge}\frac{3}{2}$ in the presence of a localized magnetic impurity atom is proved realistic. Specifying (as a mere example) a system of ultracold 22Na^{22}\mathrm{Na}22Na Fermi gas and a trapped 6Li^{6}\mathrm{Li}6Li impurity, the mechanism of exchange interaction between the Na and Li atoms is elucidated and the exchange constant is found to be positive (antiferromagnetic). The corresponding exchange Hamiltonian is derived, and the Kondo temperature is estimated at the order of 500 nK. Within a weak-coupling renormalization group scheme, it is shown that the coupling renormalizes to the non-Fermi-liquid fixed point. An observable displaying multichannel features even in the weak-coupling regime is the impurity magnetization that is negative for $T\ensuremath{\gg}{T}_{K}$ and becomes positive with decreasing temperature.
This thesis reports on the experimental realization of the 3D SU(N) Fermi-Hubbard model and the direct probing of the equation of state with an ultracold quantum gas of fermionic ytterbium in an optical lattice. Ultracold atoms in optical lattices constitute a flexible and highly tunable system to investigate Hamiltonians of condensed matter physics such as the Hubbard model. In particular, ytterbium atoms are ideal candidates for the realization of the Fermi-Hubbard model with SU(N)-symmetry due to a high decoupling of the nuclear spin from the electronic configuration. As a consequence of this enlarged symmetry, thermodynamic properties of the atomic sample depend on N, the number of spin components in the quantum gas, and novel, exotic phases are predicted to emerge at low temperatures. By locally probing a quantum gas of 173Yb in a 3D optical lattice, we determine the equation of state of the SU(6) and SU(3) Fermi-Hubbard model. The measurement of the equation of state allows us to obtain direct, model-independent access to the thermodynamic quantities of the lattice gas. In this way, we can characterize the crossover from a Fermi liquid to an SU(N) Mott insulator when tuning the interaction strength, and can probe the compressibility of the quantum gas in different interaction regimes. Moreover, we find a low specific entropy of the SU(6) gas below that of uncorrelated spins, indicating the presence of partial spin correlations in the atomic sample. The ability to access the equation of state of such high spin systems, as well as the low obtained entropy, represent an important step towards the realization of SU(N) spin Hamiltonians and the characterization of novel SU(N) phases.
We report on the experimental realization of a state-dependent lattice for a two-orbital fermionic quantum gas with strong interorbital spin exchange. In our state-dependent lattice, the ground and metastable excited electronic states of ^{173}Yb take the roles of itinerant and localized magnetic moments, respectively. Repulsive on-site interactions in conjunction with the tunnel mobility lead to spin exchange between mobile and localized particles, modeling the coupling term in the well-known Kondo Hamiltonian. In addition, we find that this exchange process can be tuned resonantly by varying the on-site confinement. We attribute this to a resonant coupling to center-of-mass excited bound states of one interorbital scattering channel.
It is argued that an ultracold quantum degenerate gas of ytterbium 173 Yb atoms having nuclear spin I =5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU( n >2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU( n ) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU( n >2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.