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Recent advances in the field of quantum technologies have opened up the road
for the realization of small-scale quantum simulators of lattice gauge theories
which, among other goals, aim at improving our understanding on the
non-perturbative mechanisms underlying the confinement of quarks. In this work,
considering periodically-driven arrays of Rydberg atoms in a tweezer ladder
geometry, we devise a scalable Floquet scheme for the quantum simulation of the
real-time dynamics in a $\mathbb{Z}_2$ LGT. Resorting to an external magnetic
field to tune the angular dependence of the Rydberg dipolar interactions, and
by a suitable tuning of the driving parameters, we manage to suppress the main
gauge-violating terms, and show that an observation of gauge-invariant
confinement dynamics in the Floquet-Rydberg setup is at reach of current
experimental techniques. Depending on the lattice size, we present a thorough
numerical test of the validity of this scheme using either exact
diagonalization or matrix-product-state algorithms for the
periodically-modulated real-time dynamics.
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