Fluctuation thermometry of an atom-resolved quantum gas: Beyond the fluctuation-dissipation theorem

Precise temperature estimation in ultracold quantum systems is crucial to improve our understanding of many-body physics. We report on a thermometry technique for quantum gases in continuous space, based on the measure of atom number fluctuations at the single-atom level via quantum gas microscopy, with the only precondition being the knowledge of the density-density correlations. We validate this method by achieving precise temperature measurements globally and locally on ideal Fermi gases for a large range of temperatures: from nearly zero temperature to several times the Fermi temperature. At low temperatures, our approach reveals striking deviations from fluctuation-dissipation predictions, revealing sub-extensive fluctuations. Our thermometry method is applicable to systems with any trapping potential and only requires local thermal equilibrium. This method enables more accurate and adaptable temperature measurements in ultracold quantum systems, opening new possibilities for studying complex many-body phenomena.