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Review: Many-body physics with individually controlled Rydberg atoms

Antoine Browaeys and Thierry Lahaye, co-founders and scientists at Pasqal, review in this paper recent developments in the field of quantum simulation with systems of individually controlled neutral atoms, interacting with each other when excited to Rydberg states. They show how they have emerged as a promising platform for this task, particularly for the simulation of spin systems. They review the techniques necessary for the manipulation of neutral atoms for the purpose of quantum simulation—such as quantum gas microscopes and arrays of optical tweezers—and explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models. We discuss recent achievements in the study of quantum many-body physics in this platform, and some current research directions beyond that.
Experimental platforms for realizing arrays of individually controlled neutral atoms. a: In a quantum gas microscope, a high- numerical-aperture objective is used to observe the fluorescence of ultracold atoms trapped in an optical lattice obtained by interfering several laser beams. 

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