Witnessing entanglement in hybrid systems

We extend the definition of entanglement witnesses based on spin structure factors to the case of scatterers with quantum mechanical motion. We show that this allows for hybrid entanglement detection and specialize the witness for a chain of trapped ions. Within this framework, we also show how the collective vibronic state of the chain can act as an undesired quantum environment affecting the spin-spin-entanglement detection. Furthermore, we investigate several specific cases where these witness operators allow us to detect hybrid entanglement.