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

Pair density waves and exotic superconductivity have long been of strong interest, and have attracted much recent attention. We present a joint theoretical and experimental exploration of possible signatures of fermion pairing with finite-momentum, or the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) order. Experimentally a doped and spin-imbalanced attractive Hubbard model is realized with a cold atomic gas in an optical lattice, and quantum gas microscopy is used to probe its properties. Computationally we study the same model with state-of-the-art constrained-path (CP) auxiliary field quantum Monte Carlo (AFQMC). Direct comparisons between experiment and computation on various short-range magnetic and charge correlations show excellent agreement. We then systematically investigate these correlations, as well as pairing correlation functions, as a function of temperature with CP-AFQMC, and determine parameter regimes in density and magnetization where signatures of FFLO order may be observed. We show that the temperature at which precursors of such an order appear is already within reach of the current experiment. We discuss routes for direct experimental detection and measurements in such states.