Dynamics of a lattice gauge theory with fermionic matter - Minimal quantum simulator with time-dependent impurities in ultracold gases

We propose aminimalmodel to study the real-time dynamics of a ℤ ₂ lattice gauge theory (LGT) coupled to fermionic matter in a cold atom quantum simulator setup. We show that dynamical correlators of the gauge fields can be measured in experiments studying the time-evolution of two pairs of impurities, and suggest the protocol for implementing the model in cold atom experiments. Further, we discuss a number of unexpected features found in the integrable limit of the model, as well as its extensions to a non-integrable case. Apotential experimental implementation of our model in the latter regime would allow one to simulate strongly-interacting LGT beyond current capabilities of classical computers.