Single-atom-resolved probing of lattice gases in momentum space

Abstract

Measuring the full distribution of individual particles is of fundamental importance to characterize many-body quantum systems through correlation functions at any order. Here, we demonstrate the possibility to reconstruct the momentum-space distribution of three-dimensional interacting lattice gases atom by atom. This is achieved by detecting individual metastable $^{4}\mathrm{He}^{*}$ atoms in the far-field regime of expansion, when released from an optical lattice. We benchmark our technique with quantum Monte Carlo calculations, demonstrating the ability to resolve momentum distributions of superfluids occupying ${10}^{5}$ lattice sites. It permits a direct measure of the condensed fraction across phase transitions, as we illustrate on the superfluid-to-normal transition. Our single-atom-resolved approach opens a route to investigate interacting lattice gases through momentum correlations.