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arXiv:1308.3208 · Physical Review Letters

SU(3) Orbital Kondo Effect with Ultracold Atoms

Yusuke Nishida

Published Sep 25, 2013• 81 citations
arXivHTMLPDF

Abstract

We propose a simple but novel scheme to realize the Kondo effect with ultracold atoms. Our system consists of a Fermi sea of spinless fermions interacting with an impurity atom of different species which is confined by an isotropic potential. The interspecies attraction can be tuned with an s-wave Feshbach resonance so that the impurity atom and a spinless fermion form a bound dimer that occupies a threefold-degenerate p orbital of the confinement potential. Many-body scatterings of this dimer and surrounding spinless fermions occur with exchanging their angular momenta and thus exhibit the SU(3) orbital Kondo effect. The associated Kondo temperature has a universal leading exponent given by TK∝exp[-π/(3apkF3)] that depends only on an effective p-wave scattering volume ap and a Fermi wave vector kF. We also elucidate a Kondo singlet formation at zero temperature and an anisotropic interdimer interaction mediated by surrounding spinless fermions. The Kondo effect thus realized in ultracold atom experiments may be observed as an increasing atom loss by lowering the temperature or with radio-frequency spectroscopy. Our scheme and its extension to a dense Kondo lattice will be useful to develop new insights into yet unresolved aspects of Kondo physics.

DOI
10.1103/physrevlett.111.135301

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We propose a simple but novel scheme to realize the Kondo effect with ultracold atoms. Our system consists of a Fermi sea of spinless fermions interacting with an impurity atom of different species which is confined by an isotropic potential. The interspecies attraction can be tuned with an s-wave Feshbach resonance so that the impurity atom and a spinless fermion form a bound dimer that occupies a threefold-degenerate p orbital of the confinement potential. Many-body scatterings of this dimer and surrounding spinless fermions occur with exchanging their angular momenta and thus exhibit the SU(3) orbital Kondo effect. The associated Kondo temperature has a universal leading exponent given by TK∝exp[-π/(3apkF3)] that depends only on an effective p-wave scattering volume ap and a Fermi wave vector kF. We also elucidate a Kondo singlet formation at zero temperature and an anisotropic interdimer interaction mediated by surrounding spinless fermions. The Kondo effect thus realized in ultracold atom experiments may be observed as an increasing atom loss by lowering the temperature or with radio-frequency spectroscopy. Our scheme and its extension to a dense Kondo lattice will be useful to develop new insights into yet unresolved aspects of Kondo physics.
The Kondo effect in condensed-matter systems manifests itself most sharply in their transport measurements. Here we propose an analogous transport signature of the orbital Kondo effect realized with ultracold atoms. Our system consists of imbalanced Fermi seas of two components of fermions and an impurity atom of different species which is confined by an isotropic potential. We first apply a $\ensuremath{\pi}/2$ pulse to transform two components of fermions into two superposition states. Their interactions with the impurity atom then cause a ``transport'' of fermions from majority to minority superposition states, whose numbers can be measured after applying another $3\ensuremath{\pi}/2$ pulse. In particular, when the interaction of one component of fermions with the impurity atom is tuned close to a confinement-induced ppp-wave or higher partial-wave resonance, the resulting conductance is shown to exhibit the Kondo signature, i.e., universal logarithmic growth by lowering the temperature. The proposed transport measurement will thus provide a clear evidence of the orbital Kondo effect accessible in ultracold atom experiments and pave the way for developing new insights into Kondo physics.
We propose a novel realization of Kondo physics with ultracold atomic gases. It is based on a Fermi sea of two different hyperfine states of one atom species forming bound states with a different species, which is spatially confined in a trapping potential. We show that different situations displaying Kondo physics can be realized when Feshbach resonances between the species are tuned by a magnetic field and the trapping frequency is varied. We illustrate that a mixture of 40K and 23Na atoms can be used to generate a Kondo-correlated state and that momentum resolved radio frequency spectroscopy can provide unambiguous signatures of the formation of Kondo resonances at the Fermi energy. We discuss how tools of atomic physics can be used to investigate open questions for Kondo physics, such as the extension of the Kondo screening cloud.
We propose an experimental protocol to directly observe the Kondo effect by scattering ultracold atoms. We propose using an optical Feshbach resonance to engineer Kondo-type spin-dependent interactions in a system with ultracold 6Li^{6}\mathrm{Li}6Li and 87Rb^{87}\mathrm{Rb}87Rb gases. We calculate the momentum transferred from the 87Rb^{87}\mathrm{Rb}87Rb gas to the 6Li^{6}\mathrm{Li}6Li gas in a scattering experiment and show that it has a logarithmically enhanced temperature dependence, characteristic of the Kondo effect, and analogous to the resistivity of alloys with magnetic impurities. Experimentally detecting this enhancement will give a different perspective on the Kondo effect, and allow us to explore a rich variety of problems such as the Kondo lattice problem and heavy-fermion systems.
The relevance of magnetic impurity problems in cold atom systems depends crucially on the nature of exchange interaction between itinerant fermionic atoms and a localized impurity atom. In particular, Kondo physics occurs only if the exchange interaction is anti-ferromagnetic, and strong enough to yield high enough Kondo temperature (TK/TF≥0.1T_K/T_F \ge 0.1TK​/TF​≥0.1). Focusing, as an example, on the experimentally accessible system of ultra-cold 173^{173}173Yb atoms, it is shown that the sign and strength of an exchange interaction between an itinerant Yb(1^{1}1S0_{0}0​) atom and a trapped Yb(3^{3}3P0_{0}0​) atom can be optically controlled. Explicitly, as the light intensity increases (from zero), the exchange interaction changes from ferromagnetic to anti-ferromagnetic. When the light intensity is just below a singlet Feshbach resonance, the singlet scattering length aSa_SaS​ is large and negative, and the Kondo temperature increases sharply.
Connecting single-layer ttt-JJJ to Kondo lattice models: Exploration with cold atoms
The Kondo effect, a hallmark of many-body physics, emerges from the antiferromagnetic coupling between localized spins and conduction fermions, leading to a correlated many-body singlet state. Here we propose to use the mixed-dimensional (mixD) bilayer Hubbard geometry as a platform to study Kondo lattice physics with current ultracold atom experiments. At experimentally feasible temperatures, we predict that key features of the Kondo effect can be observed, including formation of the Kondo cloud around a single impurity and the competition of singlet formation with Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for multiple impurities, summarized in the Doniach phase diagram. Moreover, we show that the mixD platform provides a natural bridge between the Doniach phase diagram of the Kondo lattice model, relevant to heavy-fermion materials, and the phase diagram of cuprate superconductors as described by a single-layer Zhang-Rice type ttt-JJJ model: It is possible to continuously tune between the two regimes by changing the interlayer Kondo coupling. Our findings demonstrate that the direct connection between high-temperature superconductivity and heavy-fermion physics can be experimentally studied using currently available quantum simulation platforms.
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.