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][...

A variety of nanomechanical systems can now operate at the quantum limit 1-4 , making quantum phenomena more accessible for applications and providing new opportunities for exploring the fundamentals of quantum physics. Such mechanical quantum devices offer compelling opportunities for quantum-enhanced sensing and quantum information 5-7 . Furthermore, mechanical modes provide a versatile quantum bus for coupling hybrid quantum systems, supporting a quantum-coherent connection between different physical degrees of freedom 8-13 . Here, we demonstrate a nanomechanical interface between optical photons and microwave electrical signals, using a piezoelectric optomechanical crystal. We achieve coherent signal transfer between itinerant microwave and optical fields by parametric electro-optical coupling using a localized phonon mode. We perform optical tomography of electrically injected mechanical states and observe coherent interactions between microwave, mechanical and optical modes, manifested as electromechanically induced optical transparency. Our on-chip approach merges integrated photonics with microwave nanomechanics and is fully compatible with superconducting quantum circuits, potentially enabling microwave-to-optical quantum state transfer, and photonic networks of superconducting quantum bits 14-16 .In engineered quantum systems, the interactions between different physical degrees of freedom can be strongly enhanced by mode confinement in nanoscale structures. In the field of optomechanics 17 , this has recently enabled quantum-coherent coupling between optical and mechanical modes, and quantum control of mechanical motion 2-4 . The emerging possibility of mechanically mediated state transfer 11,18-22 promises a new type of quantum transducer, using nanomechanical motion to translate electrical or spin-based quantum states to photonic states, thereby creating an optical quantum interface.Here, we present a nanomechanical transducer in which a purpose-designed microwave-frequency mechanical mode generates a coupling between electrical signals at 4 GHz and optical photons at 200 THz. Strong coherent interactions between the electrical, mechanical and optical modes are enabled by combining electromechanical and optomechanical coupling in a piezoelectric optomechanical crystal. Fabricated from aluminium nitride (AlN) and monolithically integrated on-chip, the transducer is fully compatible with superconducting quantum circuits and is well suited for cryogenic operation. Operating at microwave mechanical frequencies, this device in principle allows quantum ground-state control of the mechanical mode 1 and state transfer between quantum microwave and optical channels.The transducer is illustrated in Fig. 1. A mechanically suspended beam of AlN (0.33×1×100 µm 3 ) is patterned as an optomechanical crystal, designed to support a highly localized phonon mode at 4.2 GHz and a co-localized optical mode at 196 THz with strong optomechanical coupling 3,23 . The beam also includes a pair of aluminium electrodes connected...

Optical nonlinearities offer unique possibilities for the control of light with light. A prominent example is electromagnetically induced transparency (EIT), where the transmission of a probe beam through an optically dense medium is manipulated by means of a control beam. Scaling such experiments into the quantum domain with one (or just a few) particles of light and matter will allow for the implementation of quantum computing protocols with atoms and photons, or the realization of strongly interacting photon gases exhibiting quantum phase transitions of light. Reaching these aims is challenging and requires an enhanced matter-light interaction, as provided by cavity quantum electrodynamics. Here we demonstrate EIT with a single atom quasi-permanently trapped inside a high-finesse optical cavity. The atom acts as a quantum-optical transistor with the ability to coherently control the transmission of light through the cavity. We investigate the scaling of EIT when the atom number is increased one-by-one. The measured spectra are in excellent agreement with a theoretical model. Merging EIT with cavity quantum electrodynamics and single quanta of matter is likely to become the cornerstone for novel applications, such as dynamic control of the photon statistics of propagating light fields or the engineering of Fock state superpositions of flying light pulses.