  The Fermi two-atom problem illustrates an apparent causality violation in
Quantum Field Theory which has to do with the nature of the built in
correlations in the vacuum. It has been a constant subject of theoretical
debate and discussions during the last few decades. Nevertheless, although the
issues at hand could in principle be tested experimentally, the smallness of
such apparent violations of causality in Quantum Electrodynamics prevented the
observation of the predicted effect. In the present paper we show that the
problem can be simulated within the framework of discrete systems that can be
manifested, for instance, by trapped atoms in optical lattices or trapped ions.
Unlike the original continuum case, the causal structure is no longer sharp.
Nevertheless, as we show, it is possible to distinguish between "trivial"
effects due to "direct" causality violations, and the effects associated with
Fermi's problem, even in such discrete settings. The ability to control
externally the strength of the atom-field interactions, enables us also to
study both the original Fermi problem with "bare atoms", as well as correction
in the scenario that involves "dressed" atoms. Finally, we show that in
principle, the Fermi effect can be detected using trapped ions.
