A. Stute

We demonstrate precise control of the coupling of each of two trapped ions to the mode of an optical resonator. When both ions are coupled with near-maximum strength, we generate ion--ion entanglement heralded by the detection of two orthogonally polarized cavity photons. The entanglement fidelity with respect to the Bell state $Ψ^+$ reaches $F \geq (91.9\pm2.5)%$. This result represents an important step toward distributed quantum computing with cavities linking remote atom-based registers.

Proposed quantum networks require both a quantum interface between light and matter and the coherent control of quantum states. A quantum interface can be realized by entangling the state of a single photon with the state of an atomic or solid-state quantum memory, as demonstrated in recent experiments with trapped ions, neutral atoms, atomic ensembles, and nitrogen-vacancy spins. The entangling interaction couples an initial quantum memory state to two possible light-matter states, and the atomic level structure of the memory determines the available coupling paths. In previous work, these paths' transition parameters determine the phase and amplitude of the final entangled state, unless the memory is initially prepared in a superposition state, a step that requires coherent control. Here we report the fully tunable entanglement of a single 40Ca+ ion and the polarization state of a single photon within an optical resonator. Our method, based on a bichromatic, cavity-mediated Raman transition, allows us to select two coupling paths and adjust their relative phase and amplitude. The cavity setting enables intrinsically deterministic, high-fidelity generation of any two-qubit entangled state. This approach is applicable to a broad range of candidate systems and thus presents itself as a promising method for distributing information within quantum networks.

We demonstrate several building blocks for an ion-photon interface based on a trapped Ca ion in an optical cavity. We identify a favorable experimental configuration and measure system parameters, including relative motion of the trapped ion and the resonator mode. A complete spectrum of cavity-assisted Raman transitions between the $4^{2}S_{1/2}$ and $3^{2}D_{5/2}$ manifolds is obtained. On two of these transitions, we generate orthogonally polarized cavity photons, and we demonstrate coherent manipulation of the corresponding pair of atomic states. Possible implementations of atom-photon entanglement and state mapping within the ion-cavity system are discussed.