Density-Wave Steady-State Phase Of Dissipative Ultracold Fermions With Nearest-Neighbor Interactions

In this work, we investigate the effect of local dissipation on the presence of density-wave ordering in spinful fermions with both local and nearest-neighbor interactions as described by the extended Hubbard model. We find density-wave order to be robust against decoherence effects up to a critical point where the system becomes homogeneous with no spatial ordering. Our results will be relevant for future cold-atom experiments using fermions with nonlocal interactions arising from the dressing by highly excited Rydberg states, which have finite lifetimes due to spontaneous emission processes.