Probing the non-local correlation function in a strongly interacting Bose gas with Long-range Rydberg molecule dimers

The non-local spatial correlation function, g⁽²⁾(r), can provide valuable information on the state of a many-body quantum system. Here we report measurements of g⁽²⁾(r) in ultracold atomic gases of strontium and illustrate the effects of strong atom-atom interactions. We measure g⁽²⁾(r) via the excitation rate of vibrational-ground-state ultra long-range Rydberg molecule (ULRRM) dimers, utilizing ns ¹S₀ Rydberg states that yield dimers with highly localized internuclear separations. Effects of the unusually large s-wave scattering length in ⁸⁶Sr (a=811a₀) on the correlation function are made clearly visible by comparing with the less interacting ⁸⁴Sr gas (a=123a₀). Strong suppression of g⁽²⁾(r) for separation near the scattering length due to the last pre-asymptotic node in the scattering wave function is observed in ⁸⁶Sr sample, whereas only small deviation from g⁽²⁾(r) of an ideal Bose gas is observed at the same interparticle separation for ⁸⁴Sr sample. ⁸⁶Sr probe the universal regime of the wave function where properties are only determined by the s-wave scattering length. We compare measurements to approximate expressions for the correlation function of an interacting gas.