Photoassociation of long-range $nD$ Rydberg molecules*

Cold atomic systems have opened new frontiers at the interface of atomic and molecular physics. Of particular interest are a recently discovered class of long-range, homonuclear Rydberg molecules first predicted in~[1] and observed in~[2]. In rubidium, these molecules are formed via low-energy electron scattering of the Rydberg electron from a 5S$_{1/2}$ ground-state atom that is present within the Rydberg atom's volume. The binding mostly arises from S-wave and P-wave triplet scattering. In recent work~[3], we have observed long-range homonuclear diatomic $nD$ Rydberg molecules photoassociated out of an ultracold gas of $^{87}$Rb atoms for principal quantum numbers 34$\le n \le$40. Related results have also been reported in~[4]. The measured ground-state binding energies of $^{87}$Rb$(nD+5S_{1/2})$ molecular states are larger than those of their $^{87}$Rb$(nS+5S_{1/2})$ counterparts, showing the dependence of the molecular bond on the angular momentum of the Rydberg atom. We have exhibited the transition of $^{87}$Rb$(nD+5S_{1/2})$ molecules from a molecular-binding-dominant regime at low $n$ to a fine-structure-dominant regime at high $n$ [akin to Hund's cases (a) and (c), respectively]. In our analysis~[4], we use a Fermi model that includes S-wave and P-wave singlet and triplet scattering, the fine structure coupling of the Rydberg atom and the hyperfine structure coupling of the 5S$_{1/2}$ atom. The hyperfine structure is important because it gives rise to mixed singlet-triplet potentials. \\[4pt] [1] C. H. Greene, A. S. Dickinson, and H. R. Sadeghpour, Phys. Rev. Lett. {\bf 85}, 2458 (2000). \\[0pt] [2] V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. L\"ow, and T. Pfau, Nature {\bf 458}, 1005 (2009).\\[0pt] [3] D. A. Anderson, S. A. Miller, and G. Raithel, Phys. Rev. Lett. {\bf 112}, 163201 (2014).\\[0pt] [4] A. T. Krupp, A. Gaj, J. B. Balewski, P. Ilzh\"oer, S. Hofferberth, R. L\"ow, T. Pfau, M. Kurz, and P. Schmelcher, Phys. Rev. Lett. {\bf 112}, 143008 (2014). \\[0pt] [5] D. A. Anderson, S. A. Miller, and G. Raithel, Phys. Rev. {\bf{A 90}}, 062518 (2014).