Staggered-immersion cooling of a quantum gas in optical lattices.

Cooling many-body systems to ultralow temperatures has revolutionized the field of quantum physics. In the nanokelvin regime, strongly correlated quantum gases in optical lattices provide a clean and controllable platform for studying complex many-body problems. However, the central challenge towards revealing exotic phases of matter and creating robust multi-particle entangled states is to further reduce the thermal entropy of such systems. Here we realize efficient cooling of ten thousand ultracold bosons in staggered optical lattices. By immersing Mott-insulator samples into removable superfluid reservoirs, thermal entropy is extracted from the system. Losing only less than half of the atoms, we lower the entropy of a Mott insulator by 65-fold, achieving a record-low entropy per particle of 0.0019 $ k_{text{B}}$ ($k_{text{B}}$ is the Boltzmann constant). We further engineer the samples to a defect-free array of isolated single atoms and successfully transfer it into a coherent many-body state. The present staggered-immersion cooling opens up an avenue for exploring novel quantum matters and promises practical applications in quantum information science.