  Understanding the interplay between charge and spin and its effects on
transport is a ubiquitous challenge in quantum many-body systems. In the
Fermi-Hubbard model, this interplay is thought to give rise to magnetic
polarons, whose dynamics may explain emergent properties of quantum materials
such as high-temperature superconductivity. In this work, we use a cold-atom
quantum simulator to directly observe the formation dynamics and subsequent
spreading of individual magnetic polarons. Measuring the density- and
spin-resolved evolution of a single hole in a 2D Hubbard insulator with
short-range antiferromagnetic correlations reveals fast initial delocalization
and a dressing of the spin background, indicating polaron formation. At long
times, we find that dynamics are slowed down by the spin exchange time, and
they are compatible with a polaronic model with strong density and spin
coupling. Our work enables the study of out-of-equilibrium emergent phenomena
in the Fermi-Hubbard model, one dopant at a time.
