Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments, whereas in cold gases systems, time-of-flight, and in situ absorption imaging are the standard observation techniques. However, none of these methods allow the in situ detection of spatially resolved correlation functions at the single-particle level. Here, we give a more detailed account of recent advances in the detection of correlation functions using in situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site- and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments, whereas in cold gases systems, time-of-flight, and in situ absorption imaging are the standard observation techniques. However, none of these methods allow the in situ detection of spatially resolved correlation functions at the single-particle level. Here, we give a more detailed account of recent advances in the detection of correlation functions using in situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site- and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.

Oct 1, 201334 citations

Noise and correlation measurements using single atom detection

Valentina Krachmalnicoff, Denis Boiron, A. Perrin +6 more

Mar 7, 20080 citations

Measuring correlation functions in interacting systems of cold atoms

Eugene Demler

Bulletin of the American Physical SocietyMar 16, 20060 citations

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

Hugo Cayla, Cécile Carcy, Quentin Bouton +4 more

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.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.

arXiv:1710.08392Physical Review AJun 26, 201831 citations

^{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.