Engineered nearest-neighbor interactions with doubly modulated optical lattices

Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and we predict the emergence of the nearest-neighbor interaction and density assisted tunneling. By specifically designing a bichromatic driving pattern for a one-dimensional lattice, we demonstrate that the doubly modulated fields can be tuned to realize desired quantum phases, e.g., the Mott insulator phase with selective defects and the density wave phase.