  The transport of excitations governs fundamental properties of matter.
Particularly rich physics emerges in the interplay between disorder and
environmental noise, even in small systems such as photosynthetic biomolecules.
Counterintuitively, noise can enhance coherent quantum transport, which has
been proposed as a mechanism behind the high transport efficiencies observed in
photosynthetic complexes. This effect has been called "environmental-assisted
quantum transport" (ENAQT). Here, we propose a quantum simulation of the
excitation transport in an open quantum network, taking advantage of the high
controllability of current trapped-ion experiments. Our scheme allows for the
controlled study of various different aspects of the excitation transfer,
ranging from the influence of static disorder and interaction range, over the
effect of Markovian and non-Markovian dephasing, to the impact of a continuous
insertion of excitations. Our proposal discusses experimental error sources and
realistic parameters, showing that it can be implemented in state-of-the-art
ion-chain experiments.
