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

## TL;DR

This paper introduces a Floquet-based method to simulate $ ext{Z}_2$ lattice gauge theories using ultracold atoms, enabling exploration of strongly-interacting regimes beyond traditional numerical approaches.

## Contribution

It demonstrates how to realize $ ext{Z}_2$ symmetry in a Floquet Hamiltonian with ultracold atoms, providing a new platform for quantum simulation of gauge theories.

## Key findings

- Effective Floquet Hamiltonian exhibits $ ext{Z}_2$ symmetry under resonant driving.
- Observed dynamics differ from full Hamiltonian analysis due to symmetry-breaking.
- Identifies challenges and potential solutions for symmetry preservation in Floquet simulations.

## Abstract

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