Z$_2$ topological orders in kagom\'e dipolar systems: Feedback from Rydberg quantum simulator

TL;DR

This paper explores the emergence of $Z_2$ topological order in kagome dipolar systems, proposing a lattice gauge theory framework and discussing experimental detection methods in ultracold Rydberg atom setups and related materials.

Contribution

It introduces a $Z_2$ lattice gauge theory for kagome dipolar systems and analyzes topological excitations, linking theoretical models with experimental detection strategies.

Findings

Identification of $Z_2$ topological order in kagome dipolar systems.

Construction of a lattice gauge theory describing spinon and vison excitations.

Proposed spectroscopic signatures for experimental detection.

Abstract

The mutual feedback between quantum condensed matter and cold atom physics has been quite fruitful throughout history and continues to inspire ongoing research. Motivated by the recent activities on the quantum simulation of topological orders among the ultracold Rydberg atom arrays, we consider the possibility of searching for topological orders among the dipolar quantum magnets and polar molecules with a kagom\'{e} lattice geometry. Together with other quantum interactions such as the transverse field, the dipolar interaction endows the kagom\'e system with a similar structure as the Balents-Fisher-Girvin model and thus fosters the emergence of the $\mathbb{Z}_2$ topological orders. We construct a $\mathbb{Z}_2$ lattice gauge theory to access the topological ordered phase and describe the spinon and vison excitations for the $\mathbb{Z}_2$ topological orders. We explain the spectroscopic consequences for various quantum phases as well as the experimental detection. We further discuss the rare-earth kagom\'{e} magnets, ultracold polar molecules, and cluster Mott insulators for the physical realization.