Observing Spatial Charge and Spin Correlations in a Strongly Interacting Fermi Gas

In this Letter, we explore two-dimensional attractive Fermi gases at the microscopic level by probing spatial charge and spin correlations in situ. Using atom-resolved continuum quantum gas microscopy, we directly observe fermion pairing and study the evolution of two- and three-point correlation functions as interspin attraction is increased. The precision of our measurement allows us to reveal nonlocal anticorrelations in the pair correlation function, fundamentally forbidden by the mean-field result based on BCS theory but whose existence we confirm in exact auxiliary-field quantum Monte Carlo calculations. We demonstrate that the BCS prediction is critically deficient not only in the superfluid crossover regime but also deep in the weakly attractive side. Guided by our measurements, we find a remarkable relation between two- and three-point correlations that establishes the dominant role of pair correlations. Finally, leveraging local single-pair losses, we independently characterize the short-range behavior of pair correlations, via the measurement of Tan's contact, and find excellent agreement with numerical predictions. Our measurements provide a novel microscopic view into strongly correlated two-dimensional Fermi gases in the continuum.