When shared between remote locations, entanglement opens up fundamentally new capabilities for science and technology [1,2]. Envisioned quantum networks distribute entanglement between their remote matter-based quantum nodes, in which it is stored, processed and used [1]. Pioneering experiments have shown how photons can distribute entanglement between single ions or single atoms a few ten meters apart [3,4] and between two nitrogen-vacancy centres 1 km apart [5]. Here we report on the observation of entanglement between matter (a trapped ion) and light (a photon) over 50 km of optical fibre: a practical distance to start building large-scale quantum networks. Our methods include an efficient source of light-matter entanglement via cavity-QED techniques and a quantum photon converter to the 1550 nm telecom C band. Our methods provide a direct path to entangling remote registers of quantum-logic capable trapped-ion qubits [6][7][8], and the optical atomic clock transitions that they contain [9,10], spaced by hundreds of kilometers.Our network node consists of a 40 Ca + ion in a radiofrequency linear Paul trap with an optical cavity that enhances photon collection on the 854 nm electronic dipole transition. (Figure 1). A Raman laser pulse at 393 nm triggers emission, by the ion, of a photon into the cavity via a bichromatic cavity-mediated Raman transition (CMRT) [11]. Two indistinguishable processes are driven in the CMRT, each leading to the generation of a cavity photon and resulting in entanglement between photon polarisation and the electronic qubit state of the ion of the form 1/ √ 2 (|D J=5/2, mj =−5/2 , V + |D J=5/2, mj =−3/2 , H ), with horizontal (H) and vertical (V ) photon polarisation and two metastable Zeeman states of the ion (D J, mj ) [12]. The total probability of obtaining an on-demand free-space photon out of the ion vacuum chamber (entangled with the ion) is 0.5 ±0.1 [12].While the ∼ 3 dB/km losses suffered by 854 nm photons through state-of-the-art optical fibre allows for few km internode distances, transmission over 50 km would be 10 −15 . 854 nm photons are also frequencyincompatible with other examples of quantum matter, preventing the realisation of ion-hybrid quantum systems over any distance. Single photon frequency conversion to the telecom C band (1550 nm) offers a powerful general solution: this wavelength suffers the minimum fibre transmission losses (∼ 0.18 dB/km) and is therefore an ideal choice for a standard interfacing wavelength for quantum networking. Photons from solid-state memories [14], cold gas memories [15,16], quantum dots and nitrogen-vacancy centres [17] have been converted to telecom wavelengths. Frequency conversion of photons from ions has recently been performed, including to the telecom C band (without entanglement) [18], to the telecom * ben.lanyon@uibk.ac.at, † These authors contributed equally O band with entanglement over 80 m [19] and directly to an atomic Rubidium line at 780 nm [20].We inject single-mode fibre-coupled photons from the ion into a polarisat...

Given the great success in encoding, manipulating, storing and reading-out quantum information in their electronic states, trapped atomic ions represent a powerful platform with which to build, or integrate into, the nodes of quantum networks [5,6]. Indeed, an elementary quantum network consisting of ions in two traps a few meters apart, has been entangled via travelling ultraviolet photons [7]. A challenge is that most readily-accessible photonic transitions in trapped ions lie at wavelengths that suffer significant absorption loss in materials for manipulating and guiding light, thereby limiting the internode networking distance. Another challenge is that ionic transitions are fixed and narrowband, such that, except in rare cases [8], they cannot be interfaced with other examples of quantum matter to enable new ion-hybrid quantum systems [9]. Note that frequency-distinguishable quantum systems can be linked via their photons, though at the cost of reducing the efficiency of making that link [10].The aforementioned challenges could be overcome using quantum frequency conversion (QFC) [11,12]; a nonlinear optical process in which a photon of one frequency is converted to another, whilst preserving all the quantum and classical photon properties. QFC of single photons has recently been studied in a variety of contexts [13][14][15][16][17][18] and is typically achieved using three-wave mixing in a secondorder non-linear ( 2 ) crystal. It has been shown that QFC can preserve a broad range of photon properties, including first-and second-order coherence, and pre-existing photonphoton entanglement [12,19,20]. QFC could, therefore, act as a quantum photonic adapter for trapped ions, allowing their high-energy photonic transitions to be interfaced with the lower-energy photons better suited for long-distance travel through optical fibers, or with other forms of quantum matter.Interfacing trapped ions with the telecom wavelengths of 1310 nm (O band) or 1550 nm (C band) is particularly Abstract We demonstrate polarisation-preserving frequency conversion of single-photon-level light at 854 nm, resonant with a trapped-ion transition and qubit, to the 1550-nm telecom C band. A total photon in / fiber-coupled photon out efficiency of ∼30% is achieved, for a free-running photon noise rate of ∼60 Hz. This performance would enable telecom conversion of 854 nm polarisation qubits, produced in existing trapped-ion systems, with a signal-to-noise ratio greater than 1. In combination with near-future trappedion systems, our converter would enable the observation of entanglement between an ion and a photon that has travelled more than 100 km in optical fiber: three orders of magnitude further than the state-of-the-art.