## 3 EIT Effect and Light Pulse Storage via Atomic Coherence Gratings
Within the storage lifetime, \(\tau\), the halted light pulses can be re-accelerated and retrieved by launching a readout beam, \(E_{R}\), along the propagation direction of the coupling beam, as shown in Figure 2b. The time sequence of the light pulses, including the signal, \(E_{S}\), the coupling, \(E_{C}\), the readout, \(E_{R}\), and the retrieved pulse, \(E_{S^{\prime}}\), are shown in Figure 2c. Figure 2: The schematic diagram of the light pulse storage and retrieval based on the EIT effect. (**a**) shows the storage process of light pulses in the form of atomic coherence grating at the two ground levels, \(\ket{b}\) and \(\ket{c}\), and (**b**) shows the retrieval process of the light pulse, \(E_{S^{\prime}}\), by launching a readout beam, \(E_{R}\). The solid circles indicate the populations of \(\ket{b}\) and \(\ket{c}\). The schematic temporal traces of the involved optical fields are shown in (**c**), where the upper lines indicate the on and off states of the coupling light pulse, \(E_{C}\), and the readout light pulse, \(E_{R}\), and the pulses in the bottom row represent the signal light pulse, \(E_{S}\), and the retrieved light pulse, \(E_{S^{\prime}}\), respectively. \(\Delta\)T is the storage time of the signal pulse in Pr:YSO crystal. The absorption spectrum of Pr:YSO crystal near the two-photon resonant condition is shown in (**d**). Figure 2d was adapted from reference [24]. Similar to the conventional holographic gratings, the retrieval of the stored light pulses is of high angular and spectral selectivity [24; 63], as shown in Figure 3, where the full width at half maximum (FWHM) of the angular rocking curve and the spectral detuning rocking curve were measured to be \(\sim\)1\({}^{o}\) and 2 MHz, respectively, in the 3-mm Pr:YSO crystal at 3.4 K. Angular and spectral selectivity are the requirements of the phase matching condition during the light pulse storage and retrieval process. \[\Delta\mathbf{k}=\mathbf{k}_{S}-\mathbf{k}_{C}+\mathbf{k}_{R}-\mathbf{k}_{S^{ \prime}}\,, \tag{3}\]  
where \(\mathbf{k}_{R}\) and \(\mathbf{k}_{S^{\prime}}\) correspond to the wave vectors of the readout and the retrieved light pulses, respectively. The retrieved light pulse, \(E_{S^{\prime}}\), can be viewed as a result of constructive interference of the emission \(|\mathrm{a}\rangle\rightarrow|\mathrm{c}\rangle\) of all atoms in the \(\mathbf{k}_{S^{\prime}}\) direction and is written as  
\[E_{S^{\prime}}\propto L\mathrm{sinc}(|\Delta\mathbf{k}|L/2)\,, \tag{4}\]  
where \(L\) is the field-atom interaction length. Note that the FWHM of the spectral detuning curve is much narrower than that of the volume holographic grating; this is the result of interplay between the narrow EIT spectral window and the linewidth of the laser beam. All of them are of a spectral bandwidth in the order of MHz. The angular selectivity of atomic coherence gratings is the basis for the angular multiplexing technique, which has many potential applications such as increasing the storage capacity of light pulses and allowing angularly addressable delay lines and buffer memory. [PERSON] et al. [24] demonstrated the angular multiplexing storage of light pulses and addressable multi-channel optical buffer memory in Pr:YSO crystal based on the EIT effect, as shown in Figure 4. No cross-talk among channels was observed as long as the angular distance between neighboring channels was larger than the FWHM of the angular rocking curve of atomic coherence gratings. Figure 3: The angular and spectral selectivity of the atomic coherence grating in a 3-mm Pr:YSO crystal. The open circles are the experimental results, and the red solid curves are the theoretical fits using Equation (4), where the reflectivity is defined as the energy ratio of the retrieved signal pulse to the incident signal pulse. (**a**) shows the angular rocking curve of the atomic coherence grating, while (**b**) depicts the spectral rocking curve of the atomic coherence grating.