Single-site-and single-atom-resolved measurement of correlation functions

Endres, M. and Cheneau, M. and Fukuhara, T. and Weitenberg, C. and Schauß, P. and Gross, C. and Mazza, L. and Bañuls, M. C. and Pollet, L. and Bloch, I. and Kuhr, S. (2013) Single-site-and single-atom-resolved measurement of correlation functions. Applied Physics B: Lasers and Optics, 113 (1). pp. 27-39. ISSN 0946-2171 (

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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.