  We propose a method to probe time dependent correlations of non trivial
observables in many-body ultracold lattice gases. The scheme uses a quantum
non-demolition matter-light interface, first, to map the observable of interest
on the many body system into the light and, then, to store coherently such
information into an external system acting as a quantum memory. Correlations of
the observable at two (or more) instances of time are retrieved with a single
final measurement that includes the readout of the quantum memory. Such method
brings at reach the study of dynamics of many-body systems in and out of
equilibrium by means of quantum memories in the field of quantum simulators.
