Optical investigations of coherence and relaxation dynamics of a thulium-doped yttrium gallium garnet crystal at sub-kelvin temperatures for optical quantum memory

Rare-earth ion-doped crystals are of great interest for quantum memories, a central component in future quantum repeaters. To assess the promise of 1 $\%$ Tm ^3+ -doped yttrium gallium garnet (Tm:YGG), we report measurements of optical coherence and energy-level lifetimes of its ^3 H $_6~\leftrightarrow~^3$ H _4 transition at a temperature of around 500 mK and various magnetic fields. Using spectral hole burning (SHB), we find hyperfine ground-level (Zeeman level) lifetimes of several minutes at magnetic fields of less than 1000 G. We also measure coherence time exceeding one millisecond using two-pulse photon echoes. Three-pulse photon echo and SHB measurements reveal that due to spectral diffusion, the effective coherence time reduces to a few µ s over a timescale of around two hundred seconds. Finally, temporal and frequency-multiplexed storage of optical pulses using the atomic frequency comb protocol is demonstrated. Our results suggest Tm:YGG to be promising for multiplexed photonic quantum memory for quantum repeaters.