Decoherence characterization and quantum memory design in <sup>167</sup>Er<sup>3+</sup>:Y<sub>2</sub>SiO<sub>5</sub>

Erbium-doped crystals are promising candidates for fiber-compatible quantum memories due to their optical transition in the telecommunication C-band. Here, we investigate the optical decoherence dynamics of isotopically enriched 167Er3+:Y2SiO5 (YSO) at sub-Kelvin temperatures and low magnetic fields (<1 T). We observed an optical homogeneous linwidth of 100 Hz at 100 mK and 0.2 T – significantly narrower than previous values obtained at 7 T in a sample with the same 167Er3+ concentration. We analyze the dependence of coherence properties on magnetic field orientation and temperature, identifying spectral diffusion resulted from the host spin bath as key decoherence mechanisms. We further identified that superhyperfine interactions between the 167Er3+ and the host bath spins pose challenges for long-term storage protocols requiring precise spectral tailoring. To address this issue, we propose a strategy that combined the Stark modulation memory scheme with noiseless photon echo storage protocol, which is expected to achieve spin-wave quantum storage with lower noise and higher efficiency.