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Quantum simulation has the potential to investigate gauge theories instrongly-interacting regimes, which are up to now inaccessible throughconventional numerical techniques. Here, we take a first step in this directionby implementing a Floquet-based method for studying $\mathbb{Z}_2$ latticegauge theories using two-component ultracold atoms in a double-well potential.For resonant periodic driving at the on-site interaction strength and anappropriate choice of the modulation parameters, the effective FloquetHamiltonian exhibits $\mathbb{Z}_2$ symmetry. We study the dynamics of thesystem for different initial states and critically contrast the observedevolution with a theoretical analysis of the full time-dependent Hamiltonian ofthe periodically-driven lattice model. We reveal challenges that arise due tosymmetry-breaking terms and outline potential pathways to overcome theselimitations. Our results provide important insights for future studies oflattice gauge theories based on Floquet techniques.

Floquet approach to $\mathbb{Z}_{2}$ lattice gauge theories with ultracold atoms in optical lattices