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The detailed characterization of non-trivial coherence properties ofcomposite quantum systems of increasing size is an indispensable prerequisitefor scalable quantum computation, as well as for understanding ofnonequilibrium many-body physics. Here we show how autocorrelation functions inan interacting system of phonons as well as the quantum discord betweendistinct degrees of freedoms can be extracted from a small controllable part ofthe system. As a benchmark, we show this in chains of up to 42 trapped ions, bytracing a single phonon excitation through interferometric measurements of onlya single ion in the chain. We observe the spreading and partial refocusing ofthe excitation in the chain, even on a background of thermal excitations. Wefurther show how this local observable reflects the dynamical evolution ofquantum discord between the electronic state and the vibrational degrees offreedom of the probe ion.

Local probe of single phonon dynamics in warm ion crystals