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arXiv:2505.14630 · Physical Review A

Engineering the Kondo impurity problem with alkaline-earth-atom arrays

A. Amaricci, Andrea Richaud, Massimo Capone, Nelson Darkwah Oppong, Francesco Scazza

Published Aug 11, 2025• 7 citations
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Abstract

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.

DOI
10.1103/m7l3-y2f8

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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.
We propose a scheme to realize the Kondo model with tunable anisotropy using alkaline-earth atoms in an optical lattice. The new feature of our setup is Floquet engineering of interactions using time-dependent Zeeman shifts, that can be realized either using state-dependent optical Stark shifts or magnetic fields. The properties of the resulting Kondo model strongly depend on the anisotropy of the ferromagnetic interactions. In particular, easy-plane couplings give rise to Kondo singlet formation even though microscopic interactions are all ferromagnetic. We discuss both equilibrium and dynamical properties of the system that can be measured with ultracold atoms, including the impurity spin susceptibility, the impurity spin relaxation rate, as well as the equilibrium and dynamical spin correlations between the impurity and the ferromagnetic bath atoms. We analyze the nonequilibrium time evolution of the system using a variational non-Gaussian approach, which allows us to explore coherent dynamics over both short and long timescales, as set by the bandwidth and the Kondo singlet formation, respectively. In the quench-type experiments, when the Kondo interaction is suddenly switched on, we find that real-time dynamics shows crossovers reminiscent of poor man's renormalization group flow used to describe equilibrium systems. For bare easy-plane ferromagnetic couplings, this allows us to follow the formation of the Kondo screening cloud as the dynamics crosses over from ferromagnetic to antiferromagnetic behavior. On the other side of the phase diagram, our scheme makes it possible to measure quantum corrections to the well-known Korringa law describing the temperature dependence of the impurity spin relaxation rate. Theoretical results discussed in our paper can be measured using currently available experimental techniques.
Real materials are extremely complicated, and any attempt to understand their bulk properties must begin with the appropriate choice of an idealized model, or Hamiltonian. There are many situations where such models have furnished a decisive understanding of complex quantum phenomena, such as BCS superconductivity and quantum magnetism. There are also cases, for instance the unconventional superconductivity of doped cuprates or heavy-fermion metals, where even the simplest conceivable models are intractable to current theoretical techniques. A promising route toward understanding the physics of such models is to simulate them directly with a highly controlled quantum system. Ultracold neutral atoms, polar molecules, and ions are in many ways ideally suited to this task.\nIn this thesis, we emphasize how the unique features of particular atomic and molecular sys- tems can be leveraged to access interesting physics in experimentally feasible temperature regimes. In chapter 3, we consider prospects for simulation of the Kondo lattice model using alkaline- earth atoms. In particular, we show how groundstate properties--for instance anomalous mass enhancement--can be probed by looking at far-from equilibrium dynamics, which are a standard diagnostic tool in ultracold atom experiments. Chapter 4 describes a realistic implementation of a bosonic version of the Kondo lattice model, and we show how the Kondo interaction qualitatively changes the superfluid to Mott insulator phase transition. Chapters 5, 6, and 7 are unified through an attempt to understand the effects of dissipation in many-body quantum systems. In chapter 5, our goal is mainly to understand the detrimental effects of two-body reactive collisions on dipolar molecules in a 3D optical lattice. Chapter 6 takes a rather different perspective, and shows that this type of loss naturally induces quantum correlations in the steady state of reactive fermionic molecules or alkaline earth atoms. In chapter 7, we develop an exact analytic solution for the non-equilibrium dynamics of long-ranged Ising models with Markovian decoherence. We apply our solution to the benchmarking of dynamics in an existing trapped-ion quantum simulator, which due to its large size and long-ranged, frustrated, interactions is well beyond the reach of a brute force numerical description.
Alkaline-earth-metal atoms have a long-lived electronic excited state, and when atoms in this excited state are localized in the Fermi sea of ground-state atoms by an external potential, they serve as magnetic impurities, due to the spin-exchange interaction between the excited- and the ground-state atoms. This can give rise to the Kondo effect. However, in order to achieve this effect in current atomic gas experiments, it requires the Kondo temperature to be increased to a sizable portion of the Fermi temperature. In this paper we calculate the confinement-induced resonance (CIR) for the spin-exchanging interaction between the ground and the excited states of the alkaline-earth-metal atoms and propose that the spin-exchange interaction can be strongly enhanced by utilizing the CIR. We analyze this system by the renormalization-group approach and show that near a CIR, the Kondo temperature can be significantly enhanced.
Motivated by recent theoretical and experimental advances in quantum simulations using alkaline earth (AE) atoms, we put forward a proposal to detect the Kondo physics in a cold atomic system. It has been demonstrated that the intrinsic spin-exchange interaction in AE atoms can be significantly enhanced near a confinement-induced resonance (CIR), which facilitates the simulation of Kondo physics. Since the Kondo effect appears only for antiferromagnetic coupling, we find that the conductivity of such system exhibits an asymmetry across a resonance of spin-exchange interaction. The asymmetric conductivity can serve as the smoking gun evidence for Kondo physics in the cold atom context. When an extra magnetic field ramps up, the spin-exchange process near Fermi surface is suppressed by Zee-man energy and the conductivity becomes more and more symmetric. Our results can be verified in the current experimental setup.
A recent experiment has observed Feshbach resonances between alkali and alkaline-earth-metal atoms. These Feshbach resonances are insensitive to the nuclear spin of alkaline-earth-metal atoms. Utilizing this feature, we propose to take this system as a candidate to perform quantum simulation of the Kondo effect. An alkali-metal atom can form a molecule with an alkaline-earth-metal atom with different nuclear spins, which plays the role of spin-exchange scattering responsible for the Kondo effect. Furthermore, we point out that the existence of three-body bound state and atom-molecule resonance due to the Efimov effect can enhance this spin-exchange scattering and therefore enhance the Kondo effect. We discuss this mechanism first with a three-body problem in free space and then demonstrate that the same mechanism still holds when the alkali-metal atom is localized by an external trap and becomes an impurity embedded in the alkaline-earth-metal atomic gases.