Cavity opto-mechanics studies the coupling between a mechanical oscillator and a cavity field, with the aim to shed light on the border between classical and quantum physics. Here we report on a cavity opto-mechanical system in which a collective density excitation of a Bose-Einstein condensate is shown to serve as the mechanical oscillator coupled to the cavity field. We observe that a few photons inside the ultrahigh-finesse cavity trigger a strongly driven back-action dynamics, in quantitative agreement with a cavity opto-mechanical model. With this experiment we approach the strong coupling regime of cavity opto-mechanics, where a single excitation of the mechanical oscillator significantly influences the cavity field. The work opens up new directions to investigate mechanical oscillators in the quantum regime and quantum gases with non-local coupling.Cavity opto-mechanics has played a vital role in the conceptual exploration of the boundaries between classical and quantum-mechanical systems [1]. These fundamental questions have recently found renewed interest through the experimental progress with micro-engineered mechanical oscillators. Indeed, the demonstration of laser cooling of the mechanical mode [2,3,4,5,6,7] has been a substantial step towards the quantum regime [8,9,10].In general, light affects the motional degrees of freedom of a mechanical system through the radiation pressure force, which is caused by the exchange of momentum between light and matter. In cavity opto-mechanics the radiation pressure induced interaction between a single mode of an optical cavity and a mechanical oscillator is investigated. This interaction is mediated by the optical path length of the cavity which depends on the displacement of the mechanical oscillator.New possibilities for cavity opto-mechanics are now emerging in atomic physics by combining the tools of cavity quantum electrodynamics (QED) [11,12] with those of ultracold gases. Placing an ensemble of atoms inside a high-finesse cavity dramatically enhances the atomlight interaction since the atoms collectively couple to the same light mode [13,14,15,16,17,18]. In the dispersive regime this promises an exceedingly large optomechanical coupling strength, tying the atomic motion to the evolution of the cavity field. Recently, a thermal gas prepared in a stack of nearly two-dimensional trapping potentials has been shown to couple to the cavity field by a collective center of mass mode leading to Kerr nonlinearity at low photon numbers [16] and back-action heating induced by quantum-force fluctuations [19].A crucial goal for cavity opto-mechanical systems is the preparation of the mechanical oscillator in its ground state with no thermally activated excitations present, yet at the same time providing strong coupling to the light field. Here we use a Bose-Einstein condensate as the ground state of a mechanical oscillator and thereby collective density oscillation mechanical oscillation B A FIG. 1: (A)Cavity opto-mechanical model system. A mechanical oscillator, here...

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][...

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.

The steady increase in control over individual quantum systems has backed the dream of a quantum technology that provides functionalities beyond any classical device. Two particularly promising applications have been explored during the past decade: First, photon-based quantum communication, which guarantees unbreakable encryption 1 but still has to be scaled to high rates over large distances. Second, quantum computation, which will fundamentally enhance computability 2 if it can be scaled to a large number of quantum bits. It was realized early on that a hybrid system of light and matter qubits 3 could solve the scalability problem of both fields-that of communication via quantum repeaters 4 , that of computation via an optical interconnect between smaller quantum processors 5,6 . To this end, the development of a robust two-qubit gate that allows to link distant computational nodes is "a pressing challenge" 6 . Here we demonstrate such a quantum gate between the spin state of a single trapped atom and the polarization state of an optical photon contained in a faint laser pulse. The presented gate mechanism 7 is deterministic, robust and expected to be applicable to almost any matter qubit. It is based on reflecting the photonic qubit from a cavity that provides strong light-matter coupling. To demonstrate its versatility, we use the quantum gate to create atom-photon, atom-photon-photon, and photon-photon entangled states from separable input states.We expect our experiment to break ground for various applications, including the generation of atomic 8 and photonic 9,10 cluster states, Schrödinger-cat states 11 , deterministic photonic Bell-state measurements 12 , and quantum communication using a redundant quantum parity code 13 .Since their infancy, the fields of quantum communication and quantum computation have been largely independent. For communication 1 , optical photons are employed because they allow to transmit quantum states, such as time-bin or polarization qubits, over large distances using existing telecommunication fibre technology. Quantum computation 2 , on the other hand, is typically based on single spins, either in vacuum or in specific solidstate host materials. In addition to the long coherence times these spins can exhibit, they provide deterministic interaction mechanisms that facilitate local two-qubit * gerhard.rempe@mpq.mpg.deAtom-photon quantum gate. a, Atomic level scheme on the D2 line of 87 Rb. The photonic qubit is defined in the basis of left-(| ↓ p ) and right-(| ↑ p ) circular polarization. The atomic qubit is encoded in the atomic |F, mF states | ↓ a ≡ |1, 1 and | ↑ a ≡ |2, 2 . Here, F denotes the atomic hyperfine state and mF its projection onto an external magnetic field. The cavity (blue semi-circles) is resonant with the a.c. Stark-shifted |2, 2 ↔ |3, 3 transition on the D2 line around 780 nm. Upon reflection of a photon from the cavity, the combined atom-photon state | ↑ a ↑ p (green, ⊕) acquires a phase shift of π with respect to all other states (red, ). b, Measured ...