  One of the fundamental predictions of Quantum Electrodynamics (QED) is the
spontaneous creation of particle--antiparticle pairs from vacuum in presence of
a very strong electric field. Under these extreme conditions a strongly bound
state can fetch an otherwise unobservable electron from the Dirac sea, leaving
behind a hole representing a positron. Although generally known for many
decades, the effect has not yet been demonstrated experimentally. We propose an
analogue model of the quantum Dirac field, realized by ultra--cold fermionic
atoms in an optical lattice, aiming at an experimental simulation of this
intriguing non--perturbative phenomenon. Numerical simulations demonstrate the
effect of spontaneous pair creation in the optical analogue system, in
qualitative agreement with QED: in the adiabatic regime the vacuum can be
destabilized only by supercritical fields exceeding a critical threshold.
