Probing nonlocal spatial correlations in quantum gases with ultra-long-range Rydberg molecules

We present photoexcitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in bosonic and fermionic quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wave function ${R}_{n}$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas ${g}^{(2)}({R}_{n})$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales in the range ${R}_{n}=1400--3200$ ${a}_{0}$, which are on the order of the thermal de Broglie wavelength for temperatures around 1 $\ensuremath{\mu}\mathrm{K}$. We observe bunching for a single-component Bose gas of ${}^{84}\mathrm{Sr}$ and antibunching due to Pauli exclusion at short distances for a polarized Fermi gas of ${}^{87}\mathrm{Sr}$, revealing the effects of quantum statistics.