Quantum reservoirs with ion chains

Ion chains are promising platforms for studying and simulating quantum reservoirs. One interesting feature is that their vibrational modes can mediate entanglement between two objects which are coupled through the vibrational modes of the chain. In this work we analyze entanglement between the transverse vibrations of two heavy impurity defects embedded in an ion chain, which is generated by the coupling with the chain vibrations. We verify general scaling properties of the defect dynamics and demonstrate that entanglement between the defects can be a stationary feature of these dynamics. We then analyze entanglement in chains composed of tens of ions and propose a measurement scheme which allows one to verify the existence of the predicted entangled state.