Fig. 1: Cooling ultracold atoms by transforming a low-entropy product state to strongly correlated states.

a, Schematic of the 2D Hubbard phase diagram. The lowest temperatures reported in refs. ^6,11,12,13 (grey dashed) and the estimated temperatures in this work (red band) are marked. b, To reach lower entropy, we prepare a gapped BI in contact with a gapless metallic reservoir. Entropy flows from the BI to the reservoir³¹. After isolating the two parts, the BI is transformed into a strongly correlated state of interest by dynamically changing the lattice geometry, Hubbard parameters and density, while preserving the very low entropy of the original BI. c, The BI has a filling of two atoms per site, which appear as empty sites in a parity-projected fluorescence image (left), in contrast to the dilute reservoir. We then halve the lattice filling by doubling the number of lattice sites, thereby making the BI visible (centre). The strongly correlated state at the end of the preparation spans about 340 sites, in which empty sites correspond to coherent doublon–hole pairs indicating low entropy (right). The central state of interest and reservoir are shaped by optical potentials programmed with DMDs (not shown). d, To double the number of sites, we continuously decrease the long-spacing lattice depth V_L and increase the short-spacing lattice depth V_S. This effectively splits doubly occupied sites into dimers, which are then connected to form a square lattice.