Initialisation protocol for efficient quantum memories using resolved hyperfine structure

Rare earth dopants in crystals with long-lived, resolved hyperfine structure allow sharp, isolated spectral structures to be created via optical pumping. Here, we discuss a spectral preparation process that makes use of this property to create quantum memories where high efficiency, large bandwidth and long spin-state storage times are possible simultaneously. We then demonstrate the method using an atomic frequency comb delay-line protocol in \ErYSO, showing the delay of 6~MHz bandwidth weak coherent pulses with 22\% efficiency, limited by laser instabilities and background absorption of the comb. We discuss modifications to the preparation process to reduce this absorption and to allow $O(1)$~s storage on spin state levels. Finally, we show that, by placing this crystal in an impedance-matched optical cavity, quantum memories meeting the requirements of global-scale quantum repeater networks are possible.