Matter waves in two-dimensional arbitrary atomic crystals

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, kagomé) 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.

14 pages, 20 figures

References in corpus (12)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Scattering in Mixed Dimensions with Ultracold Gases
• Universal Fermi gases in mixed dimensions
• Three-dimensional strong localization of matter waves by scattering from atoms in a lattice with a confinement-induced resonance
• Fano-Hopfield model and photonic band gaps for an arbitrary atomic lattice
• Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects
• Confinement-induced p-wave resonances from s-wave interactions
• Matter Waves in Atomic Artificial Graphene