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arXiv:2104.08550 · Frontiers of Physics

Asymmetric conductivity of the Kondo effect in cold atomic systems

Yanting Cheng, Xin Chen, Ren Zhang

Published Jul 18, 2021• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1007/s11467-021-1091-8

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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.
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.
The Kondo effect describes the spin-exchange interaction between localized impurities and itinerant fermions. The ultracold alkaline-earth atomic gas provides a natural platform for quantum simulation of the Kondo model, utilizing its long-lived clock state and the nuclear-spin exchange interaction between clock state and ground state. One of the key issue now is whether the Kondo temperature can be high enough to be reached in current experiments, for which we have proposed to use transverse confinement to confine atoms into a one-dimensional tube and to use the confinement-induced resonance to enhance Kondo coupling. In this work, we further consider the (1+0)(1+0)(1+0)-dimensional scattering problem when the clock state is further confined by an axial harmonic confinement. We show that this axial confinement for the clock-state atoms not only plays a role for localizing them, but can also act as an additional control knob to reach the confinement-induced resonance. We show that, in the presence of both the transverse and the axial confinements, the confinement-induced resonance can be reached in the practical conditions and the Kondo effect can be attainable in this system.
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.
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.
Motivated by recent progress on ultracold alkaline-earth atoms towards the goal of simulating Kondo physics, in this work we exactly solve the few-body problem of one and two trapped fermions in one dimension interacting with a localized impurity under tunable spin-exchange interaction. It is found that depending on the sign of the spin-exchange coupling, i.e., ferromagnetic (FM) or antiferromagnetic (AFM), the attractive and repulsive branches can hold different magnetic structures. For the two-fermion case, we demonstrate the Kondo screening effect for the attractive branch with AFM coupling, and show that such screening is absent for the ground state with FM coupling. Moreover, we find a sequence of FM upper branches in the AFM coupling side. These FM states are orthogonal to all other attractive branches and their wave functions feature a full spin-charge separation. The effect of an additional contact interaction and the extension of our results to many particles are also discussed. This work reveals the intriguing physics uniquely associated with the spin-exchange interaction in the few-body point of view, which can be readily explored in the experiment of ultracold alkaline-earth atoms.