  Motivated by our observation of fast echo decay and a surprising coherence
freeze, we have developed a pump-probe spectroscopy technique for vibrational
states of ultracold $^{85}$Rb atoms in an optical lattice to gain information
about the memory dynamics of the system. We use pump-probe spectroscopy to
monitor the time-dependent changes of frequencies experienced by atoms and to
characterize the probability distribution of these frequency trajectories. We
show that the inferred distribution, unlike a naive microscopic model of the
lattice, correctly predicts the main features of the observed echo decay.
