Two dimensional momentum state lattices

TL;DR

This paper extends momentum state lattices to two dimensions, proposing a scalable method to realize and explore complex tight-binding models with tunable properties in matter-wave systems.

Contribution

It introduces a practical approach for building two-dimensional momentum state lattices for atoms, enabling exploration of higher-dimensional topological and disordered phenomena.

Findings

Numerical simulations of simple 2D models demonstrate feasibility.

Potential to study topological boundary states and flux lattices.

Framework for incorporating disorder and non-Hermiticity.

Abstract

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.