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Many applications of quantum communication crucially depend on reversible transfer of quantum states between light and matter. Motivated by rapid recent developments in theory and experiment, we review research related to quantum memory based on a photon-echo approach in solid state material with emphasis on use in a quantum repeater. After introducing quantum communication, the quantum repeater concept, and properties of a quantum memory required to be useful in a quantum repeater, we describe the historical development from spin echoes, discovered in 1950, to photon-echo quantum memory. We present a simple theoretical description of the ideal protocol, and comment on the impact of a non-ideal realization on its quantum nature. We extensively discuss rare-earth-ion doped crystals and glasses as material candidates, elaborate on traditional photon-echo experiments as a test-bed for quantum state storage, and describe the current state-of-the-art of photon-echo quantum memory. Finally, we give a brief outlook on current research.The picture shows a Europium doped Y2SiO5 crystal surrounded by electrodes in the setup used for the first proof-of-principle demonstration of the novel, photon-echo based quantum memory protocol.

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We present a light-storage experiment in a praseodymium-doped crystal where the light is mapped onto an inhomogeneously broadened optical transition shaped into an atomic frequency comb. After absorption of the light the optical excitation is converted into a spin-wave excitation by a control pulse. A second control pulse reads the memory (on-demand) by reconverting the spin-wave excitation to an optical one, where the comb structure causes a photon-echo type rephasing of the dipole moments and directional retrieval of the light. This combination of photon echo and spin-wave storage allows us to store sub-microsecond (450ns) pulses for up to 20 µs. The scheme has a high potential for storing multiple temporal modes in the single photon regime, which is an important resource for future long-distance quantum communication based on quantum repeaters.A quantum memory (QM) for photons is a light-matter interface that can achieve a coherent and reversible transfer of quantum information between a light field and a material system [1]. A QM should enable efficient, highfidelity storage of non-classical states of light, which is a key resource for future quantum networks, particularly in quantum repeaters [2][3][4][5][6] that have the potential for distributing entangled states over long distances for quantum communication tasks. In order to achieve reasonable entanglement distribution rates, it has been shown that some type of multiplexing is required [4,5], using for instance independent frequency, spatial or temporal modes (multimode QM).Several types of light-matter interactions have been proposed for building a QM, for instance electromagnetically induced transparency [7][8][9][10], Raman interactions [11][12][13][14], or photon-echo techniques [15][16][17][18][19][20][21][22]. Photon echo techniques in rare-earth-ion doped crystals have an especially high multimode capacity for storing classical light [23]. Classical photon echoes are not useful, however, for single-photon storage due to inherent noise problems due to unwanted spontaneous and stimulated emission processes when storing light on a single photon level [24]. The photon-echo QM based on controlled reversible inhomogeneous broadening [15][16][17][18][19] is free of these noise problems. But this technique has a lower time-multiplexing capacity than classical photon echoes, for a given optical depth, due to loss of storage efficiency as the controlled frequency bandwidth is increased [20,25]. Some of us recently proposed a photon-echo type QM based on an atomic frequency comb (AFC) [20] that has a storage efficiency independent of the bandwidth, allowing optimal use of the inhomogeneous broadening of rare-earthdoped crystals. An AFC memory has the potential for providing multimode storage capacity [20,25] crucial to quantum repeaters. In a first experiment [21] based on this scheme we performed a light-matter interface at the single-photon level. However, the light was retrieved after a predetermined storage time, while for quantum repeaters it is crucia...

We propose a method for efficient storage and recall of arbitrary nonstationary light fields, such as, for instance, single photon time-bin qubits or intense fields, in optically dense atomic ensembles. Our approach to quantum memory is based on controlled, reversible, inhomogeneous broadening and relies on a hidden timereversal symmetry of the optical Bloch equations describing the propagation of the light field. We briefly discuss experimental realizations of our proposal.

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