A long-lived solid-state optical quantum memory for high-rate quantum repeaters

We argue that long optical storage times are required to establish entanglement at high rates over large distances using memory-based quantum repeaters. Triggered by this conclusion, we investigate the $^3$H$_6$ $leftrightarrow$ $^3$H$_4$ transition at 795.325 nm of Tm:Y$_3$Ga$_5$O$_{12}$ (Tm:YGG). Most importantly, we show that the optical coherence time can reach 1.1 ms, and, using laser pulses, we demonstrate optical storage based on the atomic frequency comb protocol up to 100 $mu$s as well as a memory decay time T$_M$ of 13.1 $mu$s. Possibilities of how to narrow the gap between the measured value of T$_m$ and its maximum of 275 $mu$s are discussed. In addition, we demonstrate quantum state storage using members of non-classical photon pairs. Our results show the potential of Tm:YGG for creating quantum memories with long optical storage times, and open the path to building extended quantum networks.