  Recently, there has been much interest in simulating quantum field theory
effects of matter and gauge fields. In a recent work [Phys. Rev. Lett. 107,
275301 (2011)] a method for simulating compact Quantum Electrodynamics (cQED)
using Bose-Einstein condensates has been suggested. We suggest an alternative
approach, which relies on single atoms in an optical lattice, carrying 2l+1
internal levels, which converges rapidly to cQED as l increases. That enables
the simulation of cQED in 2+1 dimensions in both the weak and the strong
coupling regimes, hence allowing to probe confinement as well as other
nonperturbative effects of the theory. We provide an explicit construction for
the case l=1 which is sufficient for simulating the effect of confinement
between two external static charges.
