  We propose a method for simulating 2+1-d compact lattice
quantum-electrodynamics (QED), using ultracold atoms in optical lattices. In
our model local Bose-Einstein condensates' phases correspond to the
electromagnetic vector-potential, and the fluctuations of the local number
operators represent the conjugate electric field. The gauge invariant
Kogut-Susskind Hamiltonian is obtained as an effective low energy theory. The
field is then coupled to external static charges. We show that in the strong
coupling limit this gives rise to 'electric flux-tubes' and to confinement. The
effect can be observed by measuring the local density fluctuations of the BECs.
