Quantum networks are distributed quantum many-body systems with tailored topology and controlled information exchange. They are the backbone of distributed quantum computing architectures and quantum communication. Here we present a prototype of such a quantum network based on single atoms embedded in optical cavities. We show that atom-cavity systems form universal nodes capable of sending, receiving, storing and releasing photonic quantum information. Quantum connectivity between nodes is achieved in the conceptually most fundamental way: by the coherent exchange of a single photon. We demonstrate the faithful transfer of an atomic quantum state and the creation of entanglement between two identical nodes in independent laboratories. The created nonlocal state is manipulated by local qubit rotation. This efficient cavity-based approach to quantum networking is particularly promising as it offers a clear perspective for scalability, thus paving the way towards large-scale quantum networks and their applications.Connecting individual quantum systems via quantum channels creates a quantum network with properties profoundly different from any classical network. First, the accessible state space increases exponentially with the number of constituents. Second, the distribution of quantum states across the whole network leads to nonlocal correlations. Further, the quantum channels mediate long-range or even infinite-range interactions which can be switched on and off at will. This makes quantum networks tailor-made quantum many-body systems with adjustable degrees of connectivity and arbitrary topologies, and thus powerful quantum simulators. Open questions like the scaling behaviour, percolation of entanglement [1], multi-partite entanglement [2,3] and quantum phase transitions [4-6] make quantum networks a prime theme of current theoretical and experimental research. Similarly, quantum networks form the basis of quantum communication and distributed quantum information processing architectures, with interactions taking the form of quantum logic gates [7][8][9][10].The physical implementation of quantum networks requires suitable channels and nodes. Photonic channels are well-advanced transmitters of quantum information. Optical photons can carry quantum information over long distances with almost negligible decoherence and are compatible with existing telecommunication fibre technology. The versatility of quantum networks, however, is largely defined by the capability of the network nodes. Dedicated tasks like quantum key distribution can already be achieved using send-only emitter nodes and receive-only detector nodes [11]. However, in order to fully exploit the capabilities of quantum networks, functional network nodes are required which are able to send, receive and store quantum information reversibly and efficiently.The implementation and connection of quantum nodes is a major challenge and different approaches are currently being pursued. An intensely studied example are ensembles of gas-phase atoms [12][13][...

The faithful storage of a quantum bit (qubit) of light is essential for long-distance quantum communication, quantum networking and distributed quantum computing. The required optical quantum memory must be able to receive and recreate the photonic qubit; additionally, it must store an unknown quantum state of light better than any classical device. So far, these two requirements have been met only by ensembles of material particles that store the information in collective excitations. Recent developments, however, have paved the way for an approach in which the information exchange occurs between single quanta of light and matter. This single-particle approach allows the material qubit to be addressed, which has fundamental advantages for realistic implementations. First, it enables a heralding mechanism that signals the successful storage of a photon by means of state detection; this can be used to combat inevitable losses and finite efficiencies. Second, it allows for individual qubit manipulations, opening up avenues for in situ processing of the stored quantum information. Here we demonstrate the most fundamental implementation of such a quantum memory, by mapping arbitrary polarization states of light into and out of a single atom trapped inside an optical cavity. The memory performance is tested with weak coherent pulses and analysed using full quantum process tomography. The average fidelity is measured to be 93%, and low decoherence rates result in qubit coherence times exceeding 180  microseconds. This makes our system a versatile quantum node with excellent prospects for applications in optical quantum gates and quantum repeaters.

We study the frequency splitting of the polarization eigenmodes of the fundamental transverse mode in CO 2 laser-machined, high-finesse optical Fabry-Perot cavities and investigate the influence of the geometry of the cavity mirrors. Their highly reflective surfaces are typically not rotationally symmetric but have slightly different radii of curvature along two principal axes. We observe that the eccentricity of such elliptical mirrors lifts the degeneracy of the polarization eigenmodes. The impact of the eccentricity increases for smaller radii of curvature. A model derived from corrections to the paraxial resonator theory is in excellent agreement with the measurements, showing that geometric effects are the main source of the frequency splitting of polarization modes for the type of microscopic cavity studied here. By rotating one of the mirrors around the cavity axis, the splitting can be tuned. In the case of an identical differential phase shift per mirror, it can even be eliminated, despite a nonvanishing eccentricity of each mirror. We expect our results to have important implications for many experiments in cavity quantum electrodynamics, where Fabry-Perot cavities with small mode volumes are required. [33,34] to applications in quantum information processing, such as the efficient and coherent coupling of atomic states to the polarization of single photons [35]. The latter requires degeneracy of the polarization eigenmodes, which has been achieved for Fabry-Perot cavities built from superpolished mirror substrates [36]. Microfabricated cavities, however, can have increased frequency splittings between polarization eigenmodes, as was first observed in CO 2 laser-machined resonators [10,20]. If the splitting is on the order of the linewidth of the cavity, there can be detrimental effects on all kinds of experiments [37][38][39]. There are two strategies for dealing with the splitting in cavities: to minimize it until it becomes negligible, or to increase it such that the two polarization modes are well separated [38]. In either case, it is necessary to understand and control this splitting.Two potential sources of the splitting of polarization eigenmodes in a Fabry-Perot cavity can be distinguished. The first one is birefringence of the mirror materials, usually attributed to mechanical stress [39,40]. Combined with a finite penetration depth, this leads to a polarization-dependent phase shift upon reflection. The second source is directly related to the cavity geometry. Its existence is not evident from the usual paraxial resonator theory, in which the cavity field and its resonances are described by a scalar mode function that is independent of the polarization. The paraxial theory does describe the polarization-independent splitting of higher-order transverse modes of equal order in a cavity with elliptical mirrors, but it cannot account for an additional splitting of each of these modes into a doublet via the polarization degree of freedom. Any splitting of the polarization modes thus has to originat...

Quantum repeaters promise to enable quantum networks over global distances by circumventing the exponential decrease in success probability inherent in direct photon transmission. We propose a realistic, functionally integrated quantum-repeater implementation based on single atoms in optical cavities. Entanglement is directly generated between the single-atom quantum memory and a photon at telecom wavelength. The latter is collected with high efficiency and adjustable temporal and spectral properties into a spatially well-defined cavity mode. It is heralded by a near-infrared photon emitted from a second, orthogonal cavity. Entanglement between two remote quantum memories can be generated via an optical Bell-state measurement, while we propose entanglement swapping based on a highly efficient, cavity-assisted atom-atom gate. Our quantum-repeater scheme eliminates any requirement for wavelength conversion such that only a single system is needed at each node. We investigate a particular implementation with rubidium and realistic parameters for Fabry-Perot cavities based on CO 2 laser-machined optical fibers. We show that the scheme enables the implementation of a rather simple quantum repeater that outperforms direct entanglement generation over large distances and does not require any improvements in technology beyond the state of the art.

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