  We show how interpenetrating optical lattices containing Bose-Fermi mixtures
can be constructed to emulate the thermodynamics of quantum electrodynamics
(QED). We present models of neutral atoms on lattices in 1+1, 2+1 and 3+1
dimensions whose low energy effective action reduces to that of photons coupled
to Dirac fermions of the corresponding dimensionality. We give special
attention to 2+1 dimensional electrodynamics (QED3) and discuss how two of its
most interesting features, chiral symmetry breaking and Chern-Simons physics,
could be observed experimentally.
