Optical quantum memory on atomic ensembles: physical principles, experiments and possibilities of application in a quantum repeater

We review protocols for atomic ensemble-based optical quantum memories and their experimental implementation. Our special focus is on quantum memories in rare-earth ions doped crystals with long optical and spin coherence lifetimes based on slow light and photon-echo. Current challenges and methods for obtaining high-performance quantum memory are outlined and critically analyzed. The strategies for improving optical quantum memory for application in optical quantum repeaters are discussed.