Creation of vibrationally-excited ultralong-range Rydberg molecules in polarized and unpolarized cold gases of ${}^{87}$Sr

Photoexcitation rates for creation of ultralong-range Rydberg molecules (ULRM) with 31$\lesssim n \lesssim41$ in both ground and excited vibrational levels in cold ($T\sim900$~nK) gases of polarized and unpolarized $^{87}$Sr are presented. The measured production rates of the $ν=0, 1$ and 2 vibrational levels reveal rather different $n$ dependences which are analyzed by evaluating the Franck-Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational quantum numbers are excited due to the requirement that their wavefunctions be anti-symmetric with respect to exchange. The data also demonstrate that measurements of the formation of vibrationally-excited $ν=1$ molecules can furnish a probe of pair correlations over intermediate length scales extending from $\sim20$~nm to greater than 250~nm.