# Trilobites, butterflies, and other exotic specimens of long-range Rydberg molecules

## TL;DR

This tutorial reviews the physics, structure, and experimental progress of ultra-long-range Rydberg molecules, highlighting recent theoretical and experimental advances in understanding their potential energy surfaces and behavior in external fields.

## Contribution

It provides a comprehensive overview of the current state of theory and experiment in Rydberg molecules, including new potential energy curves and insights into their structure and interactions.

## Key findings

- Collection of potential energy curves and wave functions
- Insights into polyatomic Rydberg molecule structures
- Analysis of Rydberg molecules in external fields

## Abstract

This Ph.D. tutorial discusses ultra-long-range Rydberg molecules, the exotic bound states of a Rydberg atom and one or more ground state atoms immersed in the Rydberg electron's wave function. This novel chemical bond is distinct from an ionic or covalent bond, and is accomplished by a very different mechanism: the Rydberg electron, elastically scattering off of the ground state atoms, exerts a weak attractive force sufficient to form the molecule in long-range oscillatory potential wells. In the last decade this topic has burgeoned into a vibrant and mature subfield of atomic and molecular physics following the rapidly developing capability of experiment to observe and manipulate these molecules. This tutorial focuses on three areas where this experimental progress has demanded more sophisticated theoretical descriptions: the structure of polyatomic molecules, the influence of electronic and nuclear spin, and the behavior of these molecules in external fields. The main results are a collection of potential energy curves and electronic wave functions which together describe the physics of Rydberg molecules. Additionally, to facilitate future progress in this field, this tutorial provides a general overview of the current state of experiment and theory.