Site-Resolved Observation of Charge and Spin Correlations in the 2D Fermi-Hubbard Model

The application of quantum gas microscopy to fermionic systems has allowed for rapid advances in the field of ultracold fermionic atoms in optical lattices, including site-resolved studies of metallic, Mott insulating, and band insulating states of the two-dimensional Fermi-Hubbard model. In this talk, we extend these studies to explore spatial charge and spin correlations using spin sensitive fluorescence imaging of ultracold $^{\mathrm{40}}$K atoms trapped in a square optical lattice [1]. We observe nearest-neighbor antiferromagnetic spin correlations which are maximal at half-filling, and which weaken monotonically upon doping. Correlations between singly charged sites on the other hand display non-monotonic behavior as a function of doping. At low filling, these correlations are negative, revealing the effects of Pauli blocking and strong repulsive interactions. As the filling is increased beyond a critical value however, the correlations become positive, indicating an effective attraction between holes and doublons in the system. These findings agree well with numerical linked-cluster expansion (NLCE) and determinantal quantum Monte Carlo (DQMC) calculations. [1] Cheuk et al., Science 353, 1260 (2016)