Measuring nonlocal three-body spatial correlations with Rydberg trimers in ultracold quantum gases

We measure nonlocal third-order spatial correlations in non-degenerate ultracold gases of bosonic (${}^{84}$Sr) and spin-polarized fermionic (${}^{87}$Sr) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of six (3!) in the case of bosonic ${}^{84}$Sr due to bunching, and a marked reduction for spin-polarized fermionic ${}^{87}$Sr due to anti-bunching. The experimental results are compared to theoretical predictions and good agreement is observed. The present approach opens the way to {\it{in situ}} studies of higher-order nonlocal spatial correlations in a wide array of ultracold atomic-gas systems.