  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.
