Entanglement, perhaps the most counter-intuitive feature of quantum mechanics, describes non-local correlations between quantum objects. In recent years, entanglement has emerged as a central concept in our understanding of quantum many-body physics. It allows us to characterize phases of quantum matter that cannot be distinguished by broken symmetries, such as topological states. Measuring entanglement, however, remains challenging. In the context of quantum many-body systems, entanglement is most often quantified by entanglement entropy. In this talk, I will present the first direct measurements of entanglement entropy . This has been made possible by the single-site-resolved control and detection of ultracold bosonic atoms in an optical lattice. We measure (the second order Renyi) entanglement entropy by creating and interfering two identical copies of a quantum many-body state. Experimental access to entanglement entropy opens new avenues to explore quantum many-body physics.
 Rajibul Islam et al, Nature 528, 77 (2015)