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We proposed to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. Those correlation functions directly probed the excitations of the system, which made it possible to characterize the underlying many-body states. Moreover, they contained valuable information about phase transitions where they exhibited scale invariance. We also discussed experimental imperfections and showed that a spin-echo protocol could be used to cancel slow fluctuations in the magnetic field. We explicitly considered examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long range transverse field Ising model to illustrate the technique.

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