There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

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

Two groups this week report a significant step on the long road to quantum computing: the storage and retrieval of single photons onto and from atomic quantum memories. Chaneliere et al. produced single photons from an atomic quantum memory in one lab, transported them through a 100-metre-long optical fibre and stored them for a time in a second memory. The atomic excitation was then converted back into a single photon. Previously, weak coherent laser pulses have been stopped and retrieved in atomic media, but single photons are ideal for realizing quantum bits. Eisaman et al. report a similar approach, using the coherent control technique known as electromagnetically induced transparency for the generation, transmission and storage of single photons. A third paper reports progress in another technology critical for quantum communication and computation: the storage and distribution of entangled quantum states. Chou et al. have achieved entanglement between two samples of atoms separated by 2.8 metres that jointly store one quantum bit of information. An elementary quantum network operation involves storing a qubit state in an atomic quantum memory node, and then retrieving and transporting the information through a single photon excitation to a remote quantum memory node for further storage or analysis. Implementations of quantum network operations are thus conditioned on the ability to realize matter-to-light and/or light-to-matter quantum state mappings. Here we report the generation, transmission, storage and retrieval of single quanta using two remote atomic ensembles. A single photon is generated from a cold atomic ensemble at one site 1, and is directed to another site through 100 metres of optical fibre. The photon is then converted into a single collective atomic excitation using a dark-state polariton approach2. After a programmable storage time, the atomic excitation is converted back into a single photon. This is demonstrated experimentally, for a storage time of 0.5 microseconds, by measurement of an anti-correlation parameter. Storage times exceeding ten microseconds are observed by intensity cross-correlation measurements. This storage period is two orders of magnitude longer than the time required to achieve conversion between photonic and atomic quanta. The controlled transfer of single quanta between remote quantum memories constitutes an important step towards distributed quantum networks.

Storage and retrieval of single photons transmitted between remote quantum memories

Atomic transitions afford a convenient way of storing quantum bits. However, there are few ground-state transitions suitable for use with light at telecommunication wavelengths. Now, researchers show that ensembles of cold rubidium atoms not only make good quantum memories, but can also noiselessly convert the emitted photons into and out of the telecoms band.

A quantum memory with telecom-wavelength conversion

Long-distance quantum communication via distant pairs of entangled quantum bits (qubits) is the first step towards secure message transmission and distributed quantum computing. To date, the most promising proposals require quantum repeaters to mitigate the exponential decrease in communication rate due to optical fiber losses. However, these are exquisitely sensitive to the lifetimes of their memory elements. We propose a multiplexing of quantum nodes that should enable the construction of quantum networks that are largely insensitive to the coherence times of the quantum memory elements.

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Multiplexed memory-insensitive quantum repeaters

Two independent experiments that demonstrate memories for single quantum excitations with storage times on the order of a millisecond—two orders of magnitude longer than reported so far—should help to bring practical long-distance quantum-communication networks a step closer. Quantum memories for the storage and retrieval of quantum information are extremely sensitive to environmental influences, which limits their storage times. The ground states of atoms and ions are potential candidates for quantum memories, but although coherence times of the order of a few seconds for atoms1,2 and hundreds of seconds for ions3,4,5 have been demonstrated, long-lived storage and retrieval of single quantum excitations remains an outstanding challenge. Here, we report a quantum memory using the magnetically insensitive clock transition in atomic rubidium confined in a one-dimensional optical lattice. We observe quantum memory lifetimes exceeding 6 ms, more than two orders of magnitude longer than previously reported6. This advance is an important step towards the realization of long-distance quantum networks and the controlled production of complex entangled states of matter and light.

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Long-lived quantum memory

We report observations of entanglement of two remote atomic qubits, achieved by generating an entangled state of an atomic qubit and a single photon at site , transmitting the photon to site in an adjacent laboratory through an optical fiber, and converting the photon into an atomic qubit. Entanglement of the two remote atomic qubits is inferred by performing, locally, quantum state transfer of each of the atomic qubits onto a photonic qubit and subsequent measurement of polarization correlations in violation of the Bell inequality [EQUATION: SEE TEXT]. We experimentally determine [EQUATION: SEE TEXT]. Entanglement of two remote atomic qubits, each qubit consisting of two independent spin wave excitations, and reversible, coherent transfer of entanglement between matter and light represent important advances in quantum information science.

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Stewart D. Jenkins

Papers

Storage and retrieval of single photons transmitted between remote quantum memories

A quantum memory with telecom-wavelength conversion

Multiplexed memory-insensitive quantum repeaters

Long-lived quantum memory

Entanglement of remote atomic qubits