Trapped ions constitute one of the most promising systems for the demonstration of quantum computing protocols. By coupling trapped ions to a high-finesse optical cavity, we create a quantum interface between photons and atoms, allowing coherent transfer of quantum information between light and matter. We propose to demonstrate atom-photon entanglement, atom-atom entanglement between two ions within a cavity, and quantum state mapping from atom to photon. In addition, we discuss plans to bring ion-trap cavity quantum electrodynamics into the strong coupling regime. These would represent significant steps toward a quantum network, which could link individual quantum systems over long distances.
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