Quantum simulation of spontaneous pair creation in 2D optical lattices

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.