  Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, we
construct a quantum simulator for a U(1) gauge theory coupled to fermionic
matter. The construction is based on quantum links which realize continuous
gauge symmetry with discrete quantum variables. At low energies, quantum link
models with staggered fermions emerge from a Hubbard-type model which can be
quantum simulated. This allows us to investigate string breaking as well as the
real-time evolution after a quench in gauge theories, which are inaccessible to
classical simulation methods.
