Quantum networks provide opportunities and challenges across a range of intellectual and technical frontiers, including quantum computation, communication and metrology. The realization of quantum networks composed of many nodes and channels requires new scientific capabilities for generating and characterizing quantum coherence and entanglement. Fundamental to this endeavour are quantum interconnects, which convert quantum states from one physical system to those of another in a reversible manner. Such quantum connectivity in networks can be achieved by the optical interactions of single photons and atoms, allowing the distribution of entanglement across the network and the teleportation of quantum states between nodes.

The quantum internet

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.

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Linear optical quantum computing with photonic qubits

Single trapped ions represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling, and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.

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Quantum dynamics of single trapped ions

Cavity quantum electrodynamics (QED) systems allow the study of a variety of fundamental quantum-optics phenomena, such as entanglement, quantum decoherence and the quantum–classical boundary. Such systems also provide test beds for quantum information science. Nearly all strongly coupled cavity QED experiments have used a single atom in a high-quality-factor (high-Q) cavity. Here we report the experimental realization of a strongly coupled system in the solid state: a single quantum dot embedded in the spacer of a nanocavity, showing vacuum-field Rabi splitting exceeding the decoherence linewidths of both the nanocavity and the quantum dot. This requires a small-volume cavity and an atomic-like two-level system. The photonic crystal slab nanocavity—which traps photons when a defect is introduced inside the two-dimensional photonic bandgap by leaving out one or more holes—has both high Q and small modal volume V, as required for strong light–matter interactions. The quantum dot has two discrete energy levels with a transition dipole moment much larger than that of an atom, and it is fixed in the nanocavity during growth.

Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity

The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is based on the use of atomic ensembles as quantum memories, in combination with linear optical techniques and photon counting to perform all required operations. Here the theoretical and experimental status quo of this very active field are reviewed. The potentials of different approaches are compared quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.

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Quantum repeaters based on atomic ensembles and linear optics

The controlled production of single photons is of fundamental and practical interest; they represent the lowest excited quantum states of the radiation field, and have applications in quantum cryptography and quantum information processing. Common approaches use the fluorescence of single ions, single molecules, colour centres and semiconductor quantum dots. However, the lack of control over such irreversible emission processes precludes the use of these sources in applications (such as quantum networks) that require coherent exchange of quantum states between atoms and photons. The necessary control may be achieved in principle in cavity quantum electrodynamics. Although this approach has been used for the production of single photons from atoms, such experiments are compromised by limited trapping times, fluctuating atomfield coupling and multi-atom effects. Here we demonstrate a single-photon source based on a strongly localized single ion in an optical cavity. The ion is optimally coupled to a well-defined field mode, resulting in the generation of single-photon pulses with precisely defined shape and timing. We have confirmed the suppression of two-photon events up to the limit imposed by fluctuations in the rate of detector dark counts. The stream of emitted photons is uninterrupted over the storage time of the ion, as demonstrated by a measurement of photon correlations over 90 min.

Continuous generation of single photons with controlled waveform in an ion-trap cavity system

Quantum computing with trapped ions

In near-field imaging, resolution beyond the diffraction limit of optical microscopy is obtained by scanning the sampling region with a probe of subwavelength size. In recent experiments, single molecules were used as nanoscopic probes to attain a resolution of a few tens of nanometres. Positional control of the molecular probe was typically achieved by embedding it in a crystal attached to a substrate on a translation stage. However, the presence of the host crystal inevitably led to a disturbance of the light field that was to be measured. Here we report a near-field probe with atomic-scale resolution a single calcium ion in a radio-frequency trap that causes minimal perturbation of the optical field. We measure the three-dimensional spatial structure of an optical field with a spatial resolution as high as 60 nm (determined by the residual thermal motion of the trapped ion), and scan the modes of a low-loss optical cavity over a range of up to 100 m. The precise positioning we achieve implies a deterministic control of the coupling between ion and field. At the same time, the field and the internal states of the ion are not affected by the trapping potential. Our set-up is therefore an ideal system for performing cavity quantum electrodynamics experiments with a single particle.

A single ion as a nanoscopic probe of an optical field

We present a single calcium ion, coupled to a high-finesse cavity, as an almost ideal system for the controlled generation of single photons. Photons from a pump beam are Raman-scattered by the ion into the cavity mode, which subsequently emits the photon into a well-defined output channel. In contrast with comparable atomic systems, the ion is localized at a fixed position in the cavity mode for indefinite times, enabling truly continuous operation of the device. We have performed numeric calculations to assess the performance of the system and present the first experimental indication of single-photon emission in our set-up.

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A calcium ion in a cavity as a controlled single-photon source

The three-dimensional localization of a single ion to the Lamb–Dicke limit in a radio-frequency trap has been combined with the technique of heterodyne detection to provide high-resolution spectroscopy of the fluorescent light of the ion. A coherent component with a linewidth of 0·7 Hz, corresponding to elastic scattering of the incident laser light, was observed in the heterodyne signal. The method may be extended to observe the narrow sidebands related to the secular motion in the trap, yielding information on the dynamics of the ion. Quantum properties of the fluorescent radiation can be detected by probing higher order field correlations. As an example we investigated the phenomenon of antibunching which appears as intensity anticorrelations of the emitted radiation. A measurement of intensity cross-correlations of the fluorescent light superimposed with a weak local oscillator is expected to permit the observation of squeezing in the resonance fluorescence of a single ion.

Wolfgang Lange

Papers

Continuous generation of single photons with controlled waveform in an ion-trap cavity system

Quantum computing with trapped ions

A single ion as a nanoscopic probe of an optical field

A calcium ion in a cavity as a controlled single-photon source

Heterodyne measurement of the resonance fluorescence of a single ion