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 we review the theoretical and experimental status quo of this very active field. We compare the potential of different approaches quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.

An efficient multimode quantum memory is a crucial resource for long-distance quantum communication based on quantum repeaters. We propose a quantum memory based on spectral shaping of an inhomogeneously broadened optical transition into an atomic frequency comb ͑AFC͒. The spectral width of the AFC allows efficient storage of multiple temporal modes without the need to increase the absorption depth of the storage material, in contrast to previously known quantum memories. Efficient readout is possible thanks to rephasing of the atomic dipoles due to the AFC structure. Long-time storage and on-demand readout is achieved by use of spin states in a lambda-type configuration. We show that an AFC quantum memory realized in solids doped with rare-earth-metal ions could store hundreds of modes or more with close to unit efficiency, for material parameters achievable today.

A critical requirement for diverse applications in Quantum Information Science is the capability to disseminate quantum resources over complex quantum networks [1,2]. For example, the coherent distribution of entangled quantum states together with quantum memory to store these states can enable scalable architectures for quantum computation [3], communication [4], and metrology [5]. As a significant step toward such possibilities, here we report observations of entanglement between two atomic ensembles located in distinct apparatuses on different tables. Quantum interference in the detection of a photon emitted by one of the samples projects the otherwise independent ensembles into an entangled state with one joint excitation stored remotely in 10 5 atoms at each site [6]. After a programmable delay, we confirm entanglement by mapping the state of the atoms to optical fields and by measuring mutual coherences and photon statistics for these fields. We thereby determine a quantitative lower bound for the entanglement of the joint state of the ensembles. Our observations provide a new capability for the distribution and storage of entangled quantum states, including for scalable quantum communication networks [6].Entanglement is a uniquely quantum mechanical property of the correlations among various components of a physical system. Initial demonstrations of entanglement were made for photon pairs from the fluorescence in atomic cascades [7,8] and from parametric down conversion [9]. More recently, entanglement has been recognized as a critical resource for accomplishing tasks that are otherwise impossible in the classical domain [1]. Spectacular advances have been made in the generation of quantum entanglement for diverse physical systems [1, 2], including entanglement stored for many seconds in trapped ions for distances on the millimeter scale [10,11], long-lived entanglement of macroscopic quantum spins persisting for milliseconds on the centimeter scale [12], and remote entanglement carried by photon pairs over distances of tens of kilometers of optical fibers [13].For applications in quantum information science, entanglement can be created deterministically by way of precise control of quantum dynamics for a physical system, or probabilistically by way of quantum interference in a suitable measurement with random instances of success. In the latter case, it is essential that success be heralded unambiguously so that the resulting entangled state is available for subsequent utilization. In either case, quantum memory is required to store the entangled states until they are required for the protocol at hand.There are by now several examples of entanglement generated "on demand," [1] beginning with the realization of the EPR paradox for continuous quantum variables [14] and the deterministic entanglement of the discrete internal states of two trapped ions [15]. Important progress has been made towards measurement-induced entanglement on various fronts, including the observation of entanglement between a trapped...

Coherent and reversible mapping of quantum information between light and matter is an important experimental challenge in quantum information science. In particular, it is a decisive milestone for the implementation of quantum networks and quantum repeaters [1,2,3]. So far, quantum interfaces between light and atoms have been demonstrated with atomic gases [4,5,6,7,8,9], and with single trapped atoms in cavities [10]. Here we demonstrate the coherent and reversible mapping of a light field with less than one photon per pulse onto an ensemble of ∼ 10 7 atoms naturally trapped in a solid. This is achieved by coherently absorbing the light field in a suitably prepared solid state atomic medium [11]. The state of the light is mapped onto collective atomic excitations on an optical transition and stored for a pre-programmed time up of to 1µs before being released in a well defined spatio-temporal mode as a result of a collective interference. The coherence of the process is verified by performing an interference experiment with two stored weak pulses with a variable phase relation. Visibilities of more than 95% are obtained, which demonstrates the high coherence of the mapping process at the single photon level. In addition, we show experimentally that our interface allows one to store and retrieve light fields in multiple temporal modes. Our results represent the first observation of collective enhancement at the single photon level in a solid and open the way to multimode solid state quantum memories as a promising alternative to atomic gases.Efficient and reversible mapping of quantum states between light and matter requires strong interactions between photons and atoms. With single quantum systems, this regime can be reached with high finesse optical cavities, which is technically highly demanding [10]. In contrast, light can be efficiently absorbed in ensembles of atoms in free space. Moreover, it is possible to engineer the atomic systems such that the stored light can be retrieved in a well defined spatio-temporal mode due to a collective constructive interference between all the emitters. This collective enhancement is at the heart of protocols for storing photonic quantum states in atomic ensembles, such as schemes based on Electromagnetically-Induced Transparency (EIT) [12], off-resonant Raman interactions [2,13] and modified photon echoes using Controlled Reversible Inhomogeneous Broadening (CRIB) [14,15,16] and Atomic Frequency Combs (AFC) [11].All previous quantum storage experiments with ensembles have been performed using atomic gases as the storage material [4,5,6,7,8,9]. However, some solid state systems have properties that make them very attractive for applications in quantum storage. In particular, rare-earth ion doped solids provide a unique physical system where large ensembles of atoms are naturally trapped in a solid state matrix, which prevents decoherence due to the motion of the atoms and allows the use of trapping free protocols. Moreover, these systems also exhibit excellent coherence pro...

We propose a quantum repeater protocol which builds on the well-known DLCZ protocol [L.M. Duan, M.D. Lukin, J.I. Cirac, and P. Zoller, Nature 414, 413 (2001)], but which uses photon pair sources in combination with memories that allow to store a large number of temporal modes. We suggest to realize such multi-mode memories based on the principle of photon echo, using solids doped with rare-earth ions. The use of multimode memories promises a speedup in entanglement generation by several orders of magnitude and a significant reduction in stability requirements compared to the DLCZ protocol.The distribution of entanglement over long distances is an important challenge in quantum information. It would extend the range for tests of Bell's inequalities, quantum key distribution and quantum networks. [5,6]. A basic element of all protocols is the creation of entanglement between neighboring nodes A and B, typically conditional on the outcome of a measurement, e.g. the detection of one or more photons at a station between two nodes. In order to profit from a nested repeater protocol [1], the entanglement connection operations creating entanglement between non-neighboring nodes can only be performed once one knows the relevant measurement outcomes. This requires a communication time of order L 0 /c, where L 0 is the distance between A and B. Conventional repeater protocols are limited to a single entanglement generation attempt per elementary link per time interval L 0 /c. Here we propose to overcome this limitation using a scheme that combines photon pair sources and memories that can store a large number of distinguishable temporal modes. We also show that such memories could be realized based on the principle of photon echo, using solids doped with rare-earth ions.Our scheme is inspired by the DLCZ protocol [2], which uses Raman transitions in atomic ensembles that lead to nonclassical correlations between atomic excitations and emitted photons [7]. The basic procedure for entanglement creation between two remote locations A and B in our protocol requires one memory and one source of photon pairs at each location, denoted M A(B) and S A(B) respectively. The two sources are coherently excited such that each has a small probability p/2 of creating a pair, corresponding to a stateHere a and a ′ (b and b ′ ) are the two modes corresponding to S A (S B ), φ A (φ B ) is the phase of the pump laser at location A (B), and |0 is the vacuum state. The O(p) term introduces errors in the protocol, leading to the requirement that p has to be kept small, cf. below. The photons in modes a and b are stored in the local memories M A and M B . The modes a ′ and b ′ are coupled into fibers and combined on a beam splitter at a station between A and B. The modes after the beam splitter, where χ A,B are the phases acquired by the photons on their way to the central station. Detection of a single photon inã, for example, creates a state, where a and b are now stored in the memories. This can be rewritten as an entangled state of the two m...

Entanglement is the fundamental characteristic of quantum physics. Large experimental efforts are devoted to harness entanglement between various physical systems. In particular, entanglement between light and material systems is interesting due to their prospective roles as "flying" and stationary qubits in future quantum information technologies, such as quantum repeaters [1][2][3] and quantum networks [4]. Here we report the first demonstration of entanglement between a photon at telecommunication wavelength and a single collective atomic excitation stored in a crystal. One photon from an energytime entangled pair [5] is mapped onto a crystal and then released into a well-defined spatial mode after a predetermined storage time. The other photon is at telecommunication wavelength and is sent directly through a 50 m fiber link to an analyzer. Successful transfer of entanglement to the crystal and back is proven by a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality [6] by almost three standard deviations (S = 2.64 ± 0.23). These results represent an important step towards quantum communication technologies based on solid-state devices. In particular, our resources pave the way for building efficient multiplexed quantum repeaters [7,8] for long-distance quantum networks.While single atoms [9,10] and cold atomic gases [11][12][13][14][15][16] are currently some of the most advanced light-matter quantum interfaces, there is a strong motivation to control light-matter entanglement with more practical systems, such as solid-state devices [17]. Solid-state quantum memories for photons can be implemented with cryogenically cooled crystals doped with rare-earth-metal (RE) ions [18], which have impressive coherence properties at temperatures below 4 K. These solid-state systems have the advantage of simple implementation since RE-doped crystals are widely produced for solid-state lasers, and closed-cycle cryogenic coolers are commercially available. Important progress has been made over the last years in the context of light storage into solidstate memories, including long storage times [19], high efficiency [20] and storage of light at the single photon level with high coherence and negligible noise [8,[20][21][22][23][24]. Yet, these experiments were realized with classical bright or weak coherent states of light. While this is sufficient to characterize the performances of the memory, and even to infer the quantum characteristics of the device [20,21], it is not sufficient for the implementation of more sophisticated experiments involving entanglement, as required for most applications in quantum information science. For this purpose, it is necessary to store non-classical light, in particular individual photons that are part of an entangled state. In addition, for quantum communication applications, the other part of the entangled state should be a photon at telecommunication wavelength in order to minimize loss during transmission in optical fibers.In this Letter, we report on an experiment where a phot...

Quantum memories : a review based on the European integrated project "Qubit Applications (QAP)"

Matter and energy cannot be teleported (that is, transferred from one place to another without passing through intermediate locations). However, teleportation of quantum states (the ultimate structure of objects) is possible: only the structure is teleported--the matter stays at the source side and must be already present at the final location. Several table-top experiments have used qubits (two-dimensional quantum systems) or continuous variables to demonstrate the principle over short distances. Here we report a long-distance experimental demonstration of probabilistic quantum teleportation. Qubits carried by photons of 1.3 micro m wavelength are teleported onto photons of 1.55 micro m wavelength from one laboratory to another, separated by 55 m but connected by 2 km of standard telecommunications fibre. The first (and, with foreseeable technologies, the only) application of quantum teleportation is in quantum communication, where it could help to extend quantum cryptography to larger distances.