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

Photo-excitation of ultra-long range Rydberg molecules (ULRRMs) provides a new, \textit{in situ} probe of spatial correlations in quantum gases at previously inaccessible length scales. Excitation of the ground-state dimer ULRRM measures the nonlocal pair correlation function $g^{(2)}(R)$, with $R$ tunable by changing the principal quantum number, $n$, of the target Rydberg state ($R\sim 2 n^2$). We present observations of the effects of quantum statistics, showing anti-bunching (Pauli exclusion) in a spin-polarized Fermi gas of $^{87}$Sr and bunching in a spinless Bose gas of $^{84}$Sr. We will also discuss measurement of the scattering wave function with ULRRM dimer excitation, which should display a node for internuclear separation equal to the s-wave scattering length. This length scale is accessible for resonant interactions such as between $^{84}$Sr and $^{88}$Sr ($a_{84-88}\sim1800\,a_0$).