  We present photo-excitation of ultra-long-range Rydberg molecules as a probe
of spatial correlations in quantum gases. Rydberg molecules can be created with
well-defined internuclear spacing, set by the radius of the outer lobe of the
Rydberg electron wavefunction $R_n$. 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 ranging from $R_n = 1400 - 3200$ $a_0$, which are on the order of the
thermal de Broglie wavelength for temperatures around 1 $\mu$K. We observe
bunching for a single-component Bose gas of $^{84}$Sr and anti-bunching due to
Pauli exclusion at short distances for a polarized Fermi gas of $^{87}$Sr,
revealing the effects of quantum statistics.
