## 2 Materials and Experimental Setup  
Rare earth elements refer to 17 specific elements in the periodic table, including fifteen lanthanides with atomic numbers from 57 to 71, scandium and yttrium. Most rare earth elements can be in the trivalent state (i.e., Ce, Pr, Nd, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb) or the divalent state (i.e., Sm, Dy and Tm), shelled by fully filled 5s, 5p or 6s when doped into crystals. The fully filled shell isolates the 4f-4f transitions from the environmental disturbances; therefore, the rare earth ions have a long decoherence time and energy-level lifetime, usually in the order of microseconds or milliseconds, indicating that rare earth ions are ideal candidates for quantum memories. To further minimize the influence from the nuclear magnetic moment of crystalline lattice ions, host crystals with small nuclear magnetic moments should be selected, for example, Y\({}_{2}\)SiO\({}_{5}\), LaF\({}_{3}\), LaCl\({}_{2}\), YAlO\({}_{3}\) and LiYF\({}_{4}\) crystals [56; 58]. Praseodymium and europium are the two most-used rare earth ions in coherent quantum processing. We used Pr:YSO crystal as the material platform in the following EIT-related experiments. YSO is a monoclinic crystal and belongs to the C\({}_{2\text{h}}^{6}\) space group. The Pr\({}^{3+}\) ions have two inequivalent crystallographic sites to substitute Y\({}^{3+}\) ions, which can be marked as site 1 and site 2. In the EIT-related experiments, one usually uses the hyperfine energy levels of transition \({}^{3}\)H\({}_{4}\leftrightarrow{}^{1}\)D\({}_{2}\) of Pr\({}^{3+}\) ions. [PERSON] et al. [58] analyzed the hyperfine multiplets of the ground-state \({}^{3}\)H\({}_{4}\) and the excited-state \({}^{1}\)D\({}_{2}\) of Pr\({}^{3+}\) ions on these two different sites at 1.4 K, and those on site 1 are shown in Figure 1a. The population and dephasing lifetimes of the excited state, \({}^{1}\)D\({}_{2}\), of Pr\({}^{3+}\) ions on site 1 are T\({}_{1}=164\)\(\upmu\)s and T\({}_{2}=152\)\(\upmu\)s, respectively, while those on site 2 are T\({}_{1}=222\)\(\upmu\)s and T\({}_{2}=377\)\(\upmu\)s, respectively. The population lifetime of the hyperfine multiplets of the ground-state, \({}^{3}\)H\({}_{4}\), is in the order of 100 s [59; 60], which sets an up-limit of the storage lifetime of light pulses in Pr:YSO crystal. Here, we used 3-mm Pr:YSO crystal with a doping concentration of 0.05% (Pr\({}^{3+}\) ions on site 1) in the following experiments, and the central wavelength of the transition \({}^{3}\)H\({}_{4}\leftrightarrow{}^{1}\)D\({}_{2}\) was 605.78 nm. Figure 1: **(a)** Schematic diagram of the hyperfine multiplets of the transition \({}^{3}\)H\({}_{4}\leftrightarrow{}^{1}\)D\({}_{2}\) of Pr\({}^{3+}\) ions on site 1 in YSO crystals, in which \(|a\rangle\), \(|b\rangle\) and \(|c\rangle\) are three hyperfine energy levels to form the \(\Lambda\)-type energy level configuration for EIT-related experiments. **(b)** Schematic diagram of the experimental setup for EIT-related experiments in Pr:YSO crystals. BS: beam spliter, PBS: polarization beamsplitter, AOM: acousto-optic modulator, M1, M2, M3, M4 and M5: plane mirrors, L1: lens with a focal length \(f_{1}=30\) cm, L2: lens with a focal length \(f_{2}\) to image the output signal pulses onto the intensified charge-coupled device (iCCD). HWP: half-wave plate. The AOMs work in the double-pass configuration to eliminate the movement of the light spots, and the frequency tuning range is \(110\pm 25\) MHz. The HWP was used to change the polarization state of the three light beams. Figure 1b shows the schematic experimental setup for the EIT-related experiments. A laser beam (from a tunable dye laser 899-29, Coherent Inc., Santa Clara, USA) operating at 605.78 nm with a bandwidth of 0.5 MHz was split into three beams, serving as the probe or signal, \(E_{S}\), the coupling, \(E_{C}\), and the readout, \(E_{R}\), beams, respectively, and their intensity and frequency could be modulated by respective acousto-optic modulators (AOMs) independently.