  We show that the statistical properties of a Coulomb crystal can be measured
by means of a standard interferometric procedure performed on the spin of one
ion in the chain. The ion spin, constituted by two internal levels of the ion,
couples to the crystal modes via spatial displacement induced by photon
absorption. The loss of contrast in the interferometric signal allows one to
measure the autocorrelation function of the crystal observables. Close to the
critical point, where the chain undergoes a second-order phase transition to a
zigzag structure, the signal gives the behaviour of the correlation function at
the critical point.
