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We review the basic physics of repulsively bound atom pairs in an optical lattice, which were recently observed in the laboratory, including the theory and the experimental implementation. We also briefly discuss related many-body numerical simulations, in which time-dependent Density Matrix Renormalisation Group (DMRG) methods are used to model the many-body physics of a collection of interacting pairs, and give a comparison of the single-particle quasimomentum distribution measured in the experiment and results from these simulations. We then give a short discussion of how these repulsively bound pairs relate to bound states in some other physical systems.

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