  We show that the vibrations of a chain of trapped ions offer an interesting
route to explore the physics of disordered quantum systems. By preparing the
internal state of the ions in a quantum superposition, we show how the local
vibrational energy becomes a stochastic variable, being its statistical
properties inherited from the underlying quantum parallelism of the internal
state. We describe a minimally-perturbing measurement of the resonance
fluorescence, which allows us to study effects like Anderson localization
without the need of ground-state cooling or individual addressing, and thus
paves the way towards high-temperature ion experiments.
