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

TL;DR

This paper explores the spectral properties and ground states of laser-driven ultracold Rydberg atoms arranged in one- and two-dimensional lattices, revealing geometric influences on their static behaviors.

Contribution

It introduces a graph theory-based numerical method to determine ground states across different lattice geometries in the vanishing laser coupling limit.

Findings

Spectral structures vary between linear chains and square lattices.

Ground states depend on lattice geometry and laser detuning.

Method effectively computes ground states for various lattice configurations.

Abstract

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 discussed.