# Ultralong-range Rydberg molecules

## TL;DR

Ultralong-range Rydberg molecules are exotic bound states with large bond lengths, formed through electron-atom scattering, enabling control of molecular properties and insights into interatomic forces.

## Contribution

This review summarizes recent theoretical and experimental advances in ultralong-range Rydberg molecules, focusing on polyatomic structures, field control, and spin interactions.

## Key findings

- Potential energy surfaces exhibit oscillatory behavior reflecting Rydberg electron density.
- External fields can tune molecular properties.
- Recent progress includes experimental realization and control of polyatomic ULRMs.

## Abstract

We review ultralong-range Rydberg molecules (ULRM), which are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from multiple electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. This unconventional binding mechanism opens fascinating possibilities to tune molecular properties via weak external fields, to study spin-resolved low-energy electron-atom scattering as well as to control and to probe interatomic forces in few- and many-body systems. Here, we provide an overview on recent theoretical and experimental progress in the field with an emphasis on polyatomic ULRMs, field control and spin interactions.