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$^{171}$Yb$^{3+}$-doped Y$_2$SiO$_5$ crystals are a promising platform foroptical quantum memories in long-distance quantum communications. The relevanceof this material lies in $^{171}$Yb long optical and spin coherence times,along with a large hyperfine splitting, enabling long quantum storage overlarge bandwidths. Mechanisms affecting the optical decoherence are however notprecisely known, especially since low-temperature measurements have so farfocused on the 2 to 4 K range. In this work, we performed two- and three-pulsephoton echoes and spectral hole burning to determine optical homogeneouslinewidths in two 171 Yb:YSO crystals doped at 2 and 10 ppm. Experiments wereperformed in the 40 mK to 18 K temperature range, leading to linewidths between320 Hz, among the narrowest reported for rare-earth ions, and several MHz. Ourresults show that above 6 K the homogeneous linewidth is mainly due to anelastic two-phonon process which results in a slow broadening with temperature,the homogeneous linewidth reaching only 25 kHz at 10 K. At lower temperatures,interactions with $^{89}$Yb nuclear spin-flips, paramagnetic defects orimpurities, and also Yb-Yb interactions for the higher concentrated crystal,are likely the main limiting factor to the homogeneous linewidth. Inparticular, we conclude that the direct effect of spin and optical excitedstate lifetime is a minor contribution to optical decoherence in the wholetemperature range studied. Our results indicate possible paths and regimes forfurther decreasing the homogeneous linewidths or maintaining narrow lines athigher $^{171}$Yb concentration.

Optical coherence and spin population dynamics in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$ single crystals