Extended Data Fig. 1: Schematic of the experimental details used in the cooling protocol.

(a). The experimental sequence of the ramps used for the optical lattice and dipole potentials to initialize a BI with ultra-low entropy. (b). The experimental sequence of the ramps used for the optical lattice and dipole potentials to split the BI into a cold antiferromagnet at half-filling in the U/t = 8.3(2) Hubbard model. (c). The experimental sequence of the ramps used for the optical lattice and dipole potentials to split the BI and expand into a cold doped Hubbard system at U/t = 8.3(2). (d). Schematic of the lattice beams. Two orthogonal laser beams X and Y, whose phase are interferometrically stabilized, are retroreflected to create an interference lattice. A frequency-offseted laser beam \(\bar{X}\), co-propagating with X, are also retro-reflected to create a second lattice along the x direction shifted by half a site. (e). As we decrease the intensity of the X beam and increase the intensity of the \(\bar{X}\) beam, the interfering long-spacing lattice is ramped down and the non-interfering short-spacing lattice is ramped up. The lattice geometry changes from a long-spacing square lattice through a dimerized lattice to a short-spacing square lattice. (f). The volcano-shaped potential used in Fig. 3. A sharp, outward sloped potential facilitates preparation of the BI but prevents adiabatic expansion of the atom cloud. (g). The flattened volcano-shaped potential used in Fig. 4. Removing the potential barrier to form a flattened region allows adiabatic expansion. Each pixel of the DMD can be turned on or off. A continuous potential function is binarized using error diffusion algorithm¹¹.