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][...

We demonstrate teleportation of quantum bits between two single atoms in distant laboratories. Using a time-resolved photonic Bell-state measurement, we achieve a teleportation fidelity of (88.0± 1.5) %, largely determined by our entanglement fidelity. The low photon collection efficiency in free space is overcome by trapping each atom in an optical cavity. The resulting success probability of 0.1 % is almost 5 orders of magnitude larger than in previous experiments with remote material qubits. It is mainly limited by photon propagation and detection losses and can be enhanced with a cavity-based deterministic Bell-state measurement.The faithful transfer of quantum information between distant memories that form the nodes of a quantum network is a major goal in applied quantum science [1]. One way to achieve this is via direct transfer, e.g., by the coherent exchange of a single photon [2]. Over large distances, however, the inevitable losses in any quantum channel render this scenario unrealistic, as its efficiency decreases exponentially with the distance between the network nodes. For any classical information, the solution is simple: It can be amplified at intermediate nodes of the network. It can also be copied before transmission, allowing for a new transmission attempt should the previous one have failed. For a quantum state, the no-cloning theorem states that this is impossible. Therefore, quantum repeater schemes have been proposed to establish long-distance entanglement using photons and memories [3,4]. This entanglement can then be used as a resource for the transfer of quantum information via teleportation [5].The underlying principle of teleportation was first realized with photonic qubits [6][7][8] and since then has been exploited in many experiments [9,10]. Teleportation between matter qubits was first achieved with trapped ions [11,12], albeit over a distance limited to a few micrometers owing to the short-range Coulomb interaction. Teleportation between distant material qubits, however, requires photons distributing entanglement, as was demonstrated with two single ions separated by about 1 m [13]. The low photon-collection efficiency in free space, however, prevents scaling of that approach to larger networks. We eliminate this obstacle by trapping two remote single atoms each in an optical cavity. This allows for an in principle deterministic creation of atom-photon entanglement and atom-to-photon state mapping using a vacuum-stimulated Raman adiabatic passage (vSTI-RAP) technique [14][15][16]. To teleport the stationary qubit at the sender atom, encoded in two Zeeman states of the atomic ground-state manifold, we map it onto a photonic qubit and perform a Bell-state measurement (BSM) between this photon and that of an entangled atom-photon state originating from the receiver atom [17,18]. Compared to realizations with atoms in free space, the use of cavities boosts the overall efficiency by almost 5 orders of magnitude [13].In our experiment, single 87 Rb atoms trapped in highfinesse optical ...

The long-lived, efficient storage and retrieval of a qubit encoded on a photon is an important ingredient for future quantum networks [1,2]. Although systems with intrinsically long coherence times have been demonstrated [3][4][5][6][7][8], the combination with an efficient light-matter interface [9][10][11][12][13][14] remains an outstanding challenge. In fact, the coherence times of memories for photonic qubits are currently limited to a few milliseconds [15,16]. Here we report on a qubit memory based on a single atom coupled to a highfinesse optical resonator. By mapping and remapping the qubit between a basis used for light-matter interfacing and a basis which is less susceptible to decoherence, a coherence time exceeding 100 ms has been measured with a time-independant storage-andretrieval efficiency of 22%. This demonstrates the first photonic qubit memory with a coherence time that exceeds the lower bound needed for teleporting qubits in a global quantum internet.Photons are convenient carriers for encoding both classical and quantum information. To transport a pulse of light between the most distant locations on earth, it has to travel about 20,000 km, which takes at least 66 ms. For future quantum networks allowing for distributed quantum computations, the exchange of quantum states between network nodes is indispensable. In principle, it can be achieved by using single photons, but unavoidable losses in glass fibres in combination with the impossibility to amplify a quantum state renders the direct distribution of quantum states over long distances extremely inefficient. A possible solution is the teleportation of qubits between the end nodes of a quantum repeater link [1,17]. While teleportation can be done deterministically, another challenge occurs: as quantum teleportation requires classical communication between the end nodes, the receiver has to preserve its quantum state for at least the time it takes for the classical information to arrive [18]. This establishes the above-mentioned 66 ms as a minimum requirement for global quantum-state distribution.A qubit memory for photons has to combine a lightmatter interface used to efficiently map the qubit between the photon and a material system with the ability to preserve quantum coherence for the duration of storage. It has been shown that neutral atoms are suitable systems for both requirements [19,20] by mapping the photonic qubit onto the atom and end by recreating the photon (upward pointing red wavy arrow). a, In an elementary store-and-retrieve experiment (red area) the qubit dephases within hundreds of microseconds. The dephasing is dominantly caused by magnetic field fluctuations. This is illustrated as the deformation of the Bloch sphere which represents the qubit. The labels |F, mF denote the qubit basis states. b, By temporarily mapping the qubit to a memory basis which is less sensitive to those fluctuations, the rate of dephasing can be drastically reduced (blue area). This allows for a total storage time on the order of tens of millise...

Interference is central to quantum physics and occurs when indistinguishable paths exist, like in a double-slit experiment. Replacing the two slits with two single atoms 1 introduces optical nonlinearities for which nontrivial interference phenomena are predicted [2][3][4][5][6] . Their observation, however, has been hampered by difficulties in preparing the required atomic distribution, controlling the optical phases and detecting the faint light. Here we overcome all of these experimental challenges by combining an optical lattice for atom localisation, an imaging system with single-site resolution, and an optical resonator for light steering. We observe resonator-induced saturation of resonance fluorescence 7,8 for constructive interference of the scattered light and nonzero emission with huge photon bunching for destructive interference. The latter is explained by atomic saturation and photon pair generation 3-5 . Our experimental setting is scalable and allows one to realize the Tavis-Cummings model 9 for any number of atoms and photons, explore fundamental aspects of light-matter interaction 10-14 , and implement new quantum information processing protocols [15][16][17][18] .A multitude of non-classical radiation effects like photon antibunching 19 and squeezing 20 were predicted in the resonance fluorescence of single quantum emitters. The experimental observations of these effects 21,22 are milestones in the development of quantum optics. However, the large mismatch between the light mode driven by an emitter in free space and the light mode detected by an observer makes such quantum effects unpractical for applications. The way out is to couple the emitter to an optical resonator which enhances the interaction strength of the emitter with a tailor-made light mode. In fact, the experimental realization of well-controlled atom-cavity systems with single atoms as emitters has propelled the application potential of quantum-optical phenomena 23 enormously and, in addition, has enabled the observation of fundamentally new quantum-mechanical radiation effects induced by the cavity [24][25][26] . When scaling these single-atom systems to multiple atoms, relative optical phases appear as a new degree of freedom. As those are determined by the spatial arrangement of the atoms, both, subwavelength localisation and precise knowledge about the relative positions of the atoms, are mandatory * e-mail: stephan.ritter@mpq.mpg.de Figure 1.Experimental setup. a, A two-dimensional optical lattice is formed by a retroreflected, red-detuned 1 ○ and a blue-detuned 2 ○ laser beam in a high-finesse optical resonator 3 ○. A microscope objective 4 ○ is used to image and deterministically remove individual atoms trapped in the lattice. An atom pair is driven coherently with a running-wave beam 5 ○ propagating transversally through the resonator. Scattering from this beam into the single-sided cavity is studied via transmission through the outcoupling mirror 6 ○ as a function of the atomic positions. b, A typical fluorescence image...