## 3 EIT Effect and Light Pulse Storage via Atomic Coherence Gratings  
To demonstrate the EIT effect in Pr:YSO crystal, one should first prepare a spectrally-isolated \(\Lambda\)-type three-level ensemble, as shown in Figure 2a, in which all ions in the isolated ensemble are populated on the ground-state energy level \(\ket{b}\). This can be achieved by combining the optical pumping and spectral hole-burning techniques [24; 61]. Then, by launching a strong coupling beam, \(E_{C}\), and a weak probe beam, \(E_{S}\), into the crystal simultaneously, the absorption of the probe beam can be significantly reduced or even eliminated due to the destructive quantum interference between the two atomic transitions, \(\ket{a}\rightarrow\ket{b}\) and \(\ket{a}\rightarrow\ket{c}\), under the two-photon resonant condition, as shown in Figure 2d. According to the Kramers-Kronig relationship, the EIT effect is accompanied with a dramatic normal dispersion near the resonant frequency of the probe beam, which significantly reduces the group velocity \(v_{g}\) of the probe pulse  
\[v_{g}=\frac{d\omega_{S}}{dk_{S}}|_{\delta_{S}=0}=\frac{c}{n+\omega_{S}(\frac{ dn}{d\omega_{S}})}, \tag{1}\]  
where \(c\) is the speed of light in a vacuum; \(n\) is the refractive index of the Pr:YSO crystal at the operating wavelength, \(\lambda=605.78\) nm; \(\omega_{S}\) and \(k_{S}\) are the angular frequency and the wavenumber of the probe light, respectively; and \(\delta_{S}=\omega_{S}-\omega_{ac}\) is the frequency detuning of the probe light with respect to the resonant frequency, \(\omega_{ac}\), of the atomic transition, \(\ket{a}\rightarrow\ket{c}\), respectively. A time delay of \(\sim\)0.7 us was observed with a 5-us, 0.5-mW Gaussian probe pulse and a 5-mW coupling beam driving resonantly the \(\Lambda\)-type three-level ensemble, corresponding to a group velocity of \(4.3\times 10^{3}\) m/s in the 3-mm Pr:YSO crystal. The group velocity of light pulses in Pr:YSO crystal in the EIT condition is dependent on the coupling light intensity. One can halt and therefore store the light pulses in the EIT media by adiabatically switching off the coupling beam. This process can be explained theoretically by the concept of dark-state polaritons [62], and the signal light pulse can be mapped onto the dark-state in the form of atomic coherence grating, which is a coherent superposition of the two ground-state levels, \(\ket{b}\) and \(\ket{c}\). The amplitude of the stored spin coherence is proportional to the density matrix element \(\rho_{cb}^{0}\)[63]. \[\rho_{cb}^{0}\propto\Omega_{S}\Omega_{C}^{\pm}e^{i\mathbf{k}_{S}\cdot\mathbf{r }-i\omega_{c}t}, \tag{2}\]  
where \(\Omega_{S}=\mu_{ab}E_{S}/\hbar\) and \(\Omega_{C}=\mu_{ac}E_{C}/\hbar\) are the Rabi frequencies of the signal and the coupling light pulses, respectively, and \(\mu_{ab}\) and \(\mu_{ac}\) are the dipole moments of the corresponding atomic transitions. The superscript '\(\star\)' denotes the complex conjugate, \(\mathbf{k}_{g}=\mathbf{k}_{S}-\mathbf{k}_{C}\) is the wave vector of the atomic coherence gratings, \(\mathbf{k}_{S}\) and \(\mathbf{k}_{C}\) are the wave vectors of the signal and the coupling light pulses; \(\mathbf{r}\) is the spatial coordinate; \(\omega_{cb}\) is the resonant frequency of transition \(\ket{c}\rightarrow\ket{b}\); and \(t\) is the time coordinate. Due to various decoherence effects such as the dephasing effect and the interaction with phonons, the stored light pulses decay exponentially with a lifetime of \(\tau\), which was measured to be \(\sim\)30 us in Pr:YSO crystal at 3.4 K. The storage lifetime, \(\tau\), can be prolonged by using various techniques to decouple the hyperfine multiplets of the ground-state \({}^{3}\)H\({}_{4}\) from the environmental dephasing effects, and storage lifetimes in the order of minutes and hours were reported for Pr:YSO and Eu:YSO crystals [56; 57], respectively.