A neutral-atom Hubbard quantum simulator in the cryogenic regime

Ultracold fermionic atoms in optical lattices offer pristine realizations of Hubbard models¹, which are fundamental to modern condensed-matter physics^2,3. Despite notable advancements^4-6, the accessible temperatures in these optical lattice material analogues are still too high to address many open problems^7-10. Here we demonstrate a several-fold reduction in temperature^6,11-13, bringing large-scale quantum simulations of the Hubbard model into an entirely new regime. This is accomplished by transforming a low-entropy product state into strongly correlated states of interest via dynamic control of the model parameters^14,15, which is extremely challenging to simulate classically¹⁰. At half-filling, the long-range antiferromagnetic order is close to saturation, leading to a temperature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.0</mml:mn> <mml:msubsup><mml:mrow><mml:mn>5</mml:mn></mml:mrow> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>0.05</mml:mn></mml:mrow> <mml:mrow><mml:mo>+</mml:mo> <mml:mn>0.06</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> based on comparisons with numerically exact simulations. Doped away from half-filling, it is exceedingly challenging to realize systematically accurate and predictive numerical simulations⁹. Importantly, we are able to use quantum simulation to identify a new pathway for achieving similarly low temperatures with doping. This is confirmed by comparing short-range spin correlations to state-of-the-art, but approximate, constrained-path auxiliary-field quantum Monte Carlo simulations^16-18. Compared with the cuprates^2,19,20, the reported temperatures correspond to a reduction from far above to below room temperature, at which physics such as the pseudogap and stripe phases may be expected^3,19,21-24. Our work opens the door to quantum simulations that solve open questions in material science, develop synergies with numerical methods and theoretical studies, and lead to discoveries of new physics^8,10.