Non-local pairing and charge density wave in the attractive Fermi-Hubbard model

The 2D Fermi-Hubbard model with attractive interactions is predicted to exhibit exotic phases such as a pseudogap regime or charge density wave ordering. We explored the crossover from tightly bound to delocalized pairs, harnessing the capabilities of our quantum gas microscope, extracting the full spin and charge information with single atom resolution during each experimental run. Complete fermion pairing is observed above a critical interaction strength by vanishing total spin fluctuations, and the delocalization of the pairs can be revealed from the finite on-site spin fluctuations. In the strongly correlated regime, the size of the fermion pairs approaches the interatomic spacing, which drives the system into a charge density wave (CDW), a many-body ordered state. With the ability to address the spin and charge simultaneously, we are also able to probe the polaronic nature of a single spin moving across a background CDW. These advances pave the way to investigate the numerically intractable spin and charge doped regime of the Fermi-Hubbard model and to in-situ observe a fermionic superfluid in a lattice.