We establish a novel approach to probing spatially resolved multi-time correlation functions of interacting many-body systems, with scalable experimental overhead. Specifically, designing nonlinear measurement protocols for multidimensional spectra in a chain of trapped ions with single-site addressability enables us, e.g., to distinguish coherent from incoherent transport processes, to quantify potential anharmonicities, and to identify decoherence-free subspaces.
