Engineering of lattice models with local control in quantum microscopes

Optical lattices provide a robust platform for quantum simulations in simple geometries, and the use of superlattices and digital mirror devices (DMDs) vastly extends the control over the microscopic behavior. We use these methods to prepare exciting starting states, modify the lattice Hamiltonian, and reach full spin resolution in our quantum microscope. In particular, I will present our realization of the spin-1 Haldane model in a fermionic ladder system by engineering antiferromagnetic leg and ferromagnetic rung couplings. We measure the topological structure of the Haldane phase via the string correlations and compare them to the trivial case. Upon doping, we can use our local control to restrict the motion of holes to one dimension while keeping the spin-exchange two-dimensional. This greatly enhances hole-hole attraction leading to bound hole pairs.