The localization of phonons in ion traps with controlled quantum disorder

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, 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 such as Anderson localization without the need for ground-state cooling or individual addressing and thus paves the way for high-temperature ion experiments.