# Purely long-range polar molecules composed of identical lanthanide atoms

## TL;DR

This paper proposes a method to create purely long-range doubly polar homonuclear molecules from lanthanide atoms, enabling control of quantum states via electric and magnetic fields at ultracold temperatures.

## Contribution

It introduces a novel approach to form long-range polar molecules using lanthanide atoms with induced electric dipole moments through external fields.

## Key findings

- Potential energy curves support vibrational levels accessible by photoassociation.
- Shallow long-range wells predicted for holmium molecules.
- Method enables full quantum control of the molecules.

## Abstract

Doubly polar molecules, possessing an electric dipole moment and a magnetic dipole moment, can strongly couple to both an external electric field and a magnetic field, providing unique opportunities to exert full control of the system quantum state at ultracold temperatures. We propose a method for creating a purely long-range doubly polar homonuclear molecule from a pair of strongly magnetic lanthanide atoms, one atom being in its ground level and the other in a superposition of quasi-degenerate opposite-parity excited levels [Phys.~Rev.~Lett.~\textbf{121}, 063201 (2018)]. The electric dipole moment is induced by coupling the excited levels with an external electric field. We derive the general expression of the long-range, Stark, and Zeeman interaction energies in the properly symmetrized and fully-coupled basis describing the diatomic complex. Taking the example of holmium, our calculations predict shallow long-range wells in the potential energy curves that may support vibrational levels accessible by direct photoassociation from pairs of ground-level atoms.