  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.
