Quantum Repeaters with Photon Pair Sources and Multimode Memories

Abstract

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...

Towards an efficient atomic frequency comb quantum memory

“…In typical echo experiments only a small fraction of the input pulse is re-emitted in the echo and the storage time is not variable since it is set by the predetermined grating periodicity ∆. This is not useful for quantum repeaters where efficiencies close to 100% and on-demand read-out of the quantum memory is necessary [3]. Solutions to these issues were, however, recently proposed in Ref.…”

“…quantum cryptography) and more generally for quantum networks. This can be achieved via so-called quantum repeaters [1,2,3,4], which can overcome the exponential transmission losses in optical fiber networks. Quantum memories (QM) for photons [5,6,7,8,9] are key components in quantum repeaters, because the distribution of entanglement using photons is of probabilistic nature due to the transmission losses over long quantum channels.…”

“…For quantum repeaters a QM should be able to store single-photon states with high conditional fidelity F and with high storage and retrieval efficiency, η [4]. Further, it has recently been shown that in order to reach useful entanglement distribution rates in a repeater, QMs with multiplexing capacity (multimode QM) are necessary [3,10].…”

Control of Photon Storage Time in Photon Echoes using a Deshelving Process

“…This distance should limit applications of quantum information especially for long-distance quantum communications. To solve the limited photon transmission, a quantum repeater has been introduced for virtually unlimited transmission distance (Duan et al, 2001;Jiang et al, 2007;Simon et al, 2007;Waks et al, 2002). Quantum memory is an essential element for the entangled photon swapping in the quantum repeaters.…”

Practical photon number detection with electric field-modulated silicon avalanche photodiodes

“…M any schemes in quantum information processing [1][2][3] require that the photon number of a detected optical pulse is determined without error. For example, in quantum teleportation 4 and entanglement swapping 5 schemes used in quantum repeaters, a Bell state measurement applied upon two single photons arriving concurrently at a beam splitter requires number states N = 0, 1 or 2 to be distinguished in each detector.…”