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Photoassociation of $5snd {}^1{D}_2-5s^2 {}^1{S}_0$ ultralong-range Rydberg dimers from an ultracold ${}^{84}\mathrm{Sr}$ atomic gas in a magnetic field is studied. In the absence of magnetic fields, the electronic wave function is aligned along the rotating molecular axis through electron-atom scattering. With increasing magnetic field strength, the symmetry axis of the electron wave function becomes determined by the applied field. While the ground-state atom has no spin or net charge to interact directly with the magnetic field, the dimer wave function in the limit of strong magnetic field becomes aligned along the applied field. Photoassociation spectra show that with increasing field, an increasing number of rovibrational states are excited, indicating strong coupling between rotational states within the Rydberg dimer. 

Measurements of the production of $5snd{}^1{D}_2–5s^2{}^1{S}_0$ ultralong-range Rydberg dimers through photoassocation in an ultracold ${}^{84}\mathrm{Sr}$ atomic gas are reported. The molecular potential associated with the Rydberg $D$ state is anisotropic and the molecular states are characterized by the vibrational quantum number $\nu$ and the total angular momentum $\vec{K}=\vec{L}+\vec{N}$ , where $\vec{L}$ and $\vec{N}$ are the electronic orbital angular momentum and rotational angular momentum, respectively. The measured molecular binding energies agree reasonably well with theoretical predictions. Additionally, the electron-atom scattering leads to broader line shapes in the photoassociation spectrum than might be expected simply from the angular momentum of the initial colliding cold-atom pairs. 

We report measurements of the nonlocal two-body spatial correlation function $g^{\left(2\right)}\left(R\right)$ in an ultracold Bose gas with strong interactions using photoassociation of ultra-long-range Rydberg molecules (ULRRMs) as a spatially selective probe. This technique provides access to $g^{\left(2\right)}\left(R\right)$ on length scales from 60 to 180 nm, bridging the gap between short-range and long-range correlation measurements. The large $s$ -wave scattering length of ${}^{86}\mathrm{Sr}$ ( $a=811a_0$ ) enables exploration of the universal regime where $g^{\left(2\right)}\left(R\right)$ is governed solely by two-body interactions. Comparison with a weakly interacting isotope, ${}^{84}\mathrm{Sr}$ , highlights interaction-induced suppression of pair correlations. The measured correlation functions agree quantitatively with calculations based on the two-body reduced density matrix, without adjustable parameters. Our results establish Rydberg molecular photoassociation as a powerful tool for probing nonlocal correlations in strongly interacting quantum gases. 

Abstract Ultralong-range Rydberg molecules (ULRMs) comprise a Rydberg atom in whose electron cloud are embedded one (or more) ground-state atoms that are weakly-bound through their scattering of the Rydberg electron. The existence of such novel molecular species was first predicted theoretically in 2000 but they were not observed in the laboratory until 2009. Since that time, interest in their chemical properties, physical characteristics, and applications has increased dramatically. We discuss here recent advances in the study of ULRMs. These have yielded a wealth of information regarding low-energy electron scattering in an energy regime difficult to access using alternate techniques, and have provided a valuable probe of non-local spatial correlations in quantum gases elucidating the effects of quantum statistics. Studies in dense environments, where the Rydberg electron cloud can enclose hundreds, or even thousands, of ground-state atoms, have revealed many-body effects such as the creation of Rydberg polarons. The production of overlapping clouds of different cold atoms has enabled the creation of heteronuclear ULRMs. Indeed, the wide variety of atomic and molecular species that can now be cooled promises, through the careful choice of atomic (or molecular) species, to enable the production of ULRMs with properties tailored to meet a variety of different needs and applications.