Emergence of long distance pair coherence through incoherent local environmental coupling

We demonstrate that the interplay between a purely local incoherent environmental coupling, effectively heating up the system, and Hamiltonian dynamics generates quantum coherence. For a repulsively interacting fermionic lattice gas initially prepared in a Mott insulating state, coupling a noise field to the local spin density produces coherent fermionic pairs. We show that the formation of pair coherence is approximately diffusive with distance, and is experimentally observed in the pair momentum distribution as the formation of a sharp feature at the zone boundary.