Exploring the Kondo model in and out of equilibrium with alkaline-earth atoms

TL;DR

This paper proposes a method to realize and study the Kondo model with tunable anisotropy using ultracold alkaline-earth atoms, exploring equilibrium and non-equilibrium dynamics including Kondo singlet formation and quantum corrections.

Contribution

It introduces a Floquet engineering scheme for the Kondo model with tunable anisotropy in ultracold atoms, enabling detailed dynamical and equilibrium studies.

Findings

Observation of Kondo singlet formation with easy-plane ferromagnetic couplings

Real-time dynamics showing crossover from ferromagnetic to antiferromagnetic behavior

Measurement of quantum corrections to the Korringa law

Abstract

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 non-equilibrium 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.