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Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, weconstruct a quantum simulator for a U(1) gauge theory coupled to fermionicmatter. The construction is based on quantum links which realize continuousgauge symmetry with discrete quantum variables. At low energies, quantum linkmodels with staggered fermions emerge from a Hubbard-type model which can bequantum simulated. This allows us to investigate string breaking as well as thereal-time evolution after a quench in gauge theories, which are inaccessible toclassical simulation methods.

Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench