Spectra and ground states of one- and two-dimensional laser-driven lattices of ultracold Rydberg atoms

We investigate static properties of laser-driven ultracold Rydberg atoms confined to one- and two-dimensional uniform lattices in the limit of vanishing laser coupling. The spectral structure of square lattices is compared to those of linear chains, and similarities as well as differences are pointed out. Furthermore, we employ a method based on elements of graph theory to numerically determine the laser-detuning-dependent ground states of various lattice geometries. Ground states for chains as well as square and rectangular lattices are provided and are discussed.