In this talk, we show that interferometric techniques, such as Ramsey and spin echo,
can be used to explore dynamic correlation functions and to characterize exotic
many-body states. To illustrate the technique, we consider examples of the two-dimensional
Heisenberg antiferromagnet and the one-dimensional, long-range transverse field Ising model
which can be realized with cold atoms and trapped ions, respectively. We further
discuss a generalization of the protocol for detecting and probing many-body localized
phases in disordered spin systems. These exotic phases are characterized by a vanishing
conductivity even in the presence of interactions and at finite temperature.