Probing quantum many-body systems at the single-particle level
The manipulation and detection of individual quantum excitations forms the basis of modern quantum optics experiments. However, most of these experiments have been restricted to systems composed of only a few particles.
In recent years, tremendous experimental progress has been made in probing strongly interacting many-body systems at the level of individual particles. This was achieved using single-site- and single-atom-resolved imaging and manipulation of quantum gases in optical lattices. With this technique, ‘snapshots’ of a fluctuating many-body system are obtained, where individual excitations are directly visible and, by shining light through the imaging system, are also directly addressable.
I will review these developments and present, in more detail, a few chosen experiments: The single-site-resolved detection of correlation functions , the observation of the quantum dynamics of a mobile spin impurity , and the detection of an amplitude ‘Higgs’ mode . I will conclude with analyzing the current limitations and possible future developments, in particular, concerning the detection of entanglement in quantum many-body systems.
 M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauss, C. Gross, L. Mazza, M. C. Banuls, L. Pollet, I. Bloch and S. Kuhr, Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators, Science 334, 200 (2011)
 T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schauss, S. Hild, D. Bellem, U. Schollwock, T. Giamarchi, C. Gross, I. Bloch and S. Kuhr, Quantum dynamics of a mobile spin impurity, Nature Phys. 9, 235 (2013)
 M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauss, C. Gross, E. Demler, S. Kuhr, I. Bloch, The `Higgs' amplitude mode at the two-dimensional superfluid/Mott insulator transition, Nature 487, 454-458 (2012)