Matter waves in two-dimensional arbitrary atomic crystals

TL;DR

This paper proposes a versatile cold-atom quantum simulation platform for two-dimensional atomic crystals, enabling the study of complex lattice properties like band gaps and Dirac cones through tunable interspecies interactions.

Contribution

It introduces an exact analytic method to model matter-wave transport in 2D atomic lattices with various geometries, including disordered and finite systems.

Findings

Exact Green function determination for 2D atomic lattices

Observation of spectral features like gaps, flat bands, and Dirac cones

Tunable interspecies interactions control lattice properties

Abstract

We present a general scheme to realize a cold-atom quantum simulator of bidimensional atomic crystals. Our model is based on the use of two independently trapped atomic species: the first one, subject to a strong in-plane confinement, constitutes a two-dimensional matter wave which interacts only with atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach we show that the system Green function can be exactly determined, allowing for the investigation of the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagom\'e) lattices, studying both ideal periodic systems and experimental-size and disordered ones. Some remarkable spectral properties of these atomic artificial lattices are pointed out, such as the emergence of single and multiple gaps, flat bands, and Dirac cones. All these features can be manipulated via the interspecies interaction, which proves to be widely tunable due to the interplay between scattering length and confinements.