Relaxation of a Single Dopant in a 2D Antiferromagnetic Insulator: Interplay of Tunneling and Superexchange

The interplay between spin and density underlies much of the emergent phenomena in the doped Hubbard model, including bad metallic phases and possibly d-wave superfluidity. Quantum simulation of the Hubbard model using quantum gas microscopy offers site-resolved readout and manipulation, enabling detailed exploration of the relationship between density and spin. Here we report on the time- and position-resolved dynamics of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations using a cold-atom quantum simulator of about 400 sites. We observe an initial hole expansion determined by the tunnelling rate, followed by a slowdown that strongly depends on the spin exchange energy instead. Concurrent measurements of the spin correlations reveal a dynamical dressing of the hole by its spin environment, indicating the formation and spreading of a magnetic polaron. This work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.