  We have performed high resolution photoassociation spectroscopy of rubidium
ultra long-range Rydberg molecules in the vicinity of the 25$P$ state. Due to
the hyperfine interaction in the ground state perturber atom, the emerging
mixed singlet-triplet potentials contain contributions from both hyperfine
states. We show that this can be used to induce remote spin-flips in the
perturber atom upon excitation of a Rydberg molecule. When furthermore the
spin-orbit splitting of the Rydberg state is comparable to the hyperfine
splitting in the ground state, the orbital angular momentum of the Rydberg
electron is entangled with the nuclear spin of the perturber atom. Our results
open new possibilities for the implementation of spin-dependent interactions
for ultracold atoms in bulk systems and in optical lattices.
