Measuring correlations of cold atom systems using multiple quantum probes

We present a non-destructive method to probe a complex quantum system using multiple impurity atoms as quantum probes. Our protocol provides access to different equilibrium properties of the system by changing its coupling to the probes. In particular, we show that measurements with two probes reveal the system's non-local two-point density correlations, for probe-system contact interactions. We illustrate our findings with analytic and numerical calculations for the Bose-Hubbard model in the weakly and strongly-interacting regimes, under conditions relevant to ongoing experiments in cold atom systems.