In search of exotic pairing in the Hubbard model: Many-body computation and quantum gas microscopy.

Finite-momentum pairing, exemplified by Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, represents a paradigmatic form of unconventional superfluidity driven by Fermi-surface mismatch, but its detection in two-dimensional systems has remained elusive. Here we study a doped, spin-imbalanced attractive Hubbard model using a combined experimental and computational approach, based on quantum gas microscopy and constrained-path auxiliary-field quantum Monte Carlo, with direct comparisons showing quantitative agreement for short-range correlations at experimentally accessible temperatures. We identify broad regimes in density and magnetization where FFLO correlations emerge, and establish their finite-temperature evolution, with clear signatures of finite-momentum pairing already appearing at experimentally accessible temperatures. Spin-XY correlations are identified as a robust, directly measurable proxy for FFLO physics. Quantitative characterizations are obtained on the temperature dependence of a variety of observables and correlations, which elucidate the interplay of pairing with competing orders.