  Building on the development of momentum state lattices (MSLs) over the past
decade, we introduce a simple extension of this technique to higher dimensions.
Based on the selective addressing of unique Bragg resonances in matter-wave
systems, MSLs have enabled the realization of tight-binding models with tunable
disorder, gauge fields, non-Hermiticity, and other features. Here, we examine
and outline an experimental approach to building scalable and tunable
tight-binding models in two dimensions describing the laser-driven dynamics of
atoms in momentum space. Using numerical simulations, we highlight some of the
simplest models and types of phenomena this system is well-suited to address,
including flat-band models with kinetic frustration and flux lattices
supporting topological boundary states. Finally, we discuss many of the direct
extensions to this model, including the introduction of disorder and
non-Hermiticity, which will enable the exploration of new transport and
localization phenomena in higher dimensions.
