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arXiv:1906.08932 · Physical Review Letters

Quasiexact Kondo Dynamics of Fermionic Alkaline-Earth-Like Atoms at Finite Temperatures

Shimpei Goto, Ippei Danshita

Published Oct 3, 2019• 16 citations
arXivHTMLPDF

Abstract

A recent experiment has observed the antiferromagnetic interaction between the ground state ^{1}S_{0} and the metastable state ^{3}P_{0} of ^{171}Yb atoms, which are fermionic. This observation combined with the use of state-dependent optical lattices allows for quantum simulation of the Kondo model. We propose that in this Kondo simulator the anomalous temperature dependence of transport, namely, the Kondo effect, can be detected through quench dynamics triggered by the shift of a trap potential. For this purpose, we improve the numerical efficiency of the minimally entangled typical thermal states (METTSs) algorithm by applying additional Trotter gates. Using the improved METTSs algorithm, we compute the quench dynamics of the one-dimensional Kondo model at finite temperatures quasiexactly. We find that the center-of-mass motion exhibits a logarithmic suppression with a decrease in the temperature, which is a characteristic feature of the Kondo effect.

DOI
10.1103/physrevlett.123.143002

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A recent experiment has observed the antiferromagnetic interaction between the ground state ^{1}S_{0} and the metastable state ^{3}P_{0} of ^{171}Yb atoms, which are fermionic. This observation combined with the use of state-dependent optical lattices allows for quantum simulation of the Kondo model. We propose that in this Kondo simulator the anomalous temperature dependence of transport, namely, the Kondo effect, can be detected through quench dynamics triggered by the shift of a trap potential. For this purpose, we improve the numerical efficiency of the minimally entangled typical thermal states (METTSs) algorithm by applying additional Trotter gates. Using the improved METTSs algorithm, we compute the quench dynamics of the one-dimensional Kondo model at finite temperatures quasiexactly. We find that the center-of-mass motion exhibits a logarithmic suppression with a decrease in the temperature, which is a characteristic feature of the Kondo effect.
We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alkaline-earth-metal atoms governed by the Kondo lattice Hamiltonian plus a parabolic confining potential. In a homogenous system, this mean-field theory is believed to give a qualitatively correct description of heavy-fermion metals and Kondo insulators: It reproduces the Kondo-like scaling of the quasiparticle mass in the former and the same scaling of the excitation gap in the latter. In order to understand ground-state properties in a trap, we extend this mean-field theory via local-density approximation. We find that the Kondo insulator gap manifests as a shell structure in the trapped density profile. In addition, a strong signature of the large Fermi surface expected for heavy-fermion systems survives the confinement and could be probed in time-of-flight experiments. From a full self-consistent diagonalization of the mean-field theory, we are able to study dynamics in the trap. We find that the mass enhancement of quasiparticle excitations in the heavy-Fermi liquid phase manifests as slowing of the dipole oscillations that result from a sudden displacement of the trap center.
We demonstrate that laser excitations can coherently induce a novel Kondo effect in ultracold atoms in optical lattices. Using a model of alkaline-earth fermions with two orbitals, it is shown that the optically coupled two internal states are dynamically entangled to form the Kondo-singlet state, overcoming the heating effect due to the irradiation. Furthermore, a lack of SU(N) symmetry in the optical coupling provides a peculiar feature in the Kondo effect, which results in spin-selective renormalization of effective masses. We also discuss the effects of interorbital exchange interactions, and reveal that they induce novel crossover or reentrant behavior of the Kondo effect owing to control of the coupling anisotropy. The laser-induced Kondo effect is highly controllable by tuning the laser strength and the frequency, and thus offers a versatile platform to study the Kondo physics using ultracold atoms.
The Kondo effect may be observable in some atom-surface scattering experiments, in particular, those involving alkaline-earth atoms. By combining Keldysh techniques with the noncrossing (NCA) approximation to solve the time-dependent Newns-Anderson Hamiltonian in the $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty}$ limit, Shao, Nordlander, and Langreth found an anomalously strong surface-temperature dependence of the outgoing charge state fractions. Here we employ a dynamical 1/N1/N1/N expansion with a finite Coulomb interaction UUU to give a more realistic description of the scattering process. We test the accuracy of the 1/N1/N1/N expansion in the N=1N=1N=1 case of spinless fermions against the exact independent particle solution. We then compare results obtained in the $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty}$ limit with the NCA at N=4N=4N=4 and recover qualitative features already found. Finally, we analyze the realistic situation of Ca atoms with U=5.8U=5.8U=5.8 eV scattered off Cu(001) surfaces. Although the presence of the doubly ionized Ca2+{\mathrm{Ca}}^{2+}Ca2+ species can change the absolute scattered Ca+{\mathrm{Ca}}^{+}Ca+ yields, the temperature dependence is qualitatively the same as that found in the $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty}$ limit. One of the main difficulties that experimentalists face in attempting to detect this effect is that the atomic velocity must be kept small enough to limit kinematic smearing of the Fermi surface of the metal.
We propose quantum simulation experiments of the Kondo impurity problem using cold alkaline-earth(-like) atoms (AEAs) in a combination of optical lattice and optical tweezer potentials. Within an ab initio model for atomic interactions in the optical potentials, we analyze hallmark signatures of the Kondo effect in a variety of observables accessible in cold-atom quantum simulators. We identify additional terms not part of the textbook Kondo problem, mostly ignored in previous works and giving rise to a direct competition between spin and charge correlations, strongly suppressing Kondo physics. We show that the Kondo effect can be restored by locally adjusting the chemical potential on the impurity site, and we identify realistic parameter regimes and preparation protocols suited to current experiments with AEA arrays. Our work paves the way for quantum simulations of the Kondo problem and offers insights into Kondo physics in unconventional regimes.