Two-dimensional momentum state lattices

Cold atoms offer a clean, precise, and highly controllable platform for quantum simulation. The technique of momentum state lattices (MSLs) in one dimension allows the spectroscopic engineering of synthetic lattices with single site precision, offering independent control over all tunneling terms and site energies. In this talk, I present the extension of 1-D MSLs to engineer 2-D synthetic lattices of laser coupled atomic states. The platform of 2-D MSLs offer the potential to explore topological, disordered, and kinetically frustrated lattice models in two dimensions. Due to our experimental switch from Rb-87 to K-39, our system offers tunable interactions via magnetic Feshbach resonance. The ability to augment the aforementioned two-dimensional models with tunable interactions promises an exploration of a broad range of nonlinear lattice phenomena.