  We consider a system of ultracold atoms in an optical lattice as a quantum
simulator for electron-positron pair production in quantum electrodynamics
(QED). For a setup in one spatial dimension, we investigate the nonequilibrium
phenomenon of pair production including the backreaction leading to plasma
oscillations. Unlike previous investigations on quantum link models, we focus
on the infinite-dimensional Hilbert space of QED and show that it may be well
approximated by experiments employing Bose-Einstein condensates interacting
with fermionic atoms. The calculations based on functional integral techniques
give a unique access to the physical parameters required to realize the QED
phenomena in a cold atom experiment. In particular, we use our approach to
consider quantum link models in a yet unexplored parameter regime and give
bounds for their ability to capture essential features of the physics. The
results suggest a paradigmatic change towards realizations using coherent
many-body states rather than single atoms for quantum simulations of
high-energy particle physics phenomena.
