Ultralong-range Rydberg molecules of Hg atoms

Ultralong-range Rydberg molecules, composed of an excited Rydberg atom and a ground-state atom, are characterized by large bond lengths, dipole moments, sensitivity to external fields, and an unusual binding mechanism based on low-energy elastic electron scattering. Although Rydberg molecules formed between alkali atoms have received the most attention, the additional complexity found in atoms with more than a single valence electron poses new theoretical challenges as well as new possibilities for control and design of the molecular structure. In this paper, we extend the theory of Rydberg molecules to include the additional spin coupling of the Rydberg states of a multivalent atom. We employ this theory to describe the properties of Rydberg molecules composed of mercury atoms. We calculate the potential energy curves of both heteronuclear (${\mathrm{Hg}}^{*}\mathrm{Rb}$) and homonuclear (${\mathrm{Hg}}^{*}\mathrm{Hg}$) molecules. In the former case, we propose the realization of long-range spin entanglement and remote spin flip. In the latter, we show how long-lived metastable molecular states of ${\mathrm{Hg}}^{*}\mathrm{Hg}$ exist as resonances above the dissociation threshold.