Complex Hubbard models in quantum simulators with programmable optical lattices.

We investigate the use of programmable optical lattices for quantum simulation of Hubbard models, determining analytic expressions for the Hubbard parameters, finding that they are suitable for emulating strongly correlated systems with complex structures. Programmable potentials are highly flexible, with the ability to control the depth and shape of individual sites in the optical lattice dynamically. Quantum simulators of Hubbard models with (1) complex basis are required to represent many real materials of contemporary interest, (2) broken translational symmetry are needed to study impurity physics, and (3) complex dynamical lattices are needed to investigate strong correlation out of equilibrium. We derive analytic expressions for Hubbard Hamiltonians in programmable potential systems. We find experimental parameters for quantum simulation of Hubbard models with complex basis, concluding that programmable optical lattices are suitable for this purpose. We discuss how programmable optical lattices can be used for quantum simulation of complex compounds, impurities, and non-equilibrium physics.