Optical-lattice Hamiltonians for relativistic quantum electrodynamics

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 quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.