  Accessing new regimes in quantum simulation requires the development of new
techniques for quantum state preparation. We demonstrate the quantum state
engineering of a strongly correlated many-body state of the two-component
repulsive Fermi-Hubbard model on a square lattice. Our scheme makes use of an
ultralow entropy doublon band insulator created through entropy redistribution.
After isolating the band insulator, we change the underlying potential to
expand it into a half-filled system. The final many-body state realized shows
strong antiferromagnetic correlations and a temperature below the exchange
energy. We observe an increase in entropy, which we find is likely caused by
the many-body physics in the last step of the scheme. This technique is
promising for low-temperature studies of cold-atom-based lattice models.
