## 5 Controllable Polarization Rotator  
In quantum cryptography, or more exactly, quantum key distribution, information can be encoded onto different freedoms of photons, for instance, polarization [106; 107], frequency [108] and orbital angular momentum [27; 28; 87; 109; 110], in which polarization is one of the mostly used freedoms of photons due to its robustness and ease of operation. In the BB84 quantum key distribution protocol, the qubit in the quantum channel is encoded on different polarization bases. Therefore, controlling the polarization state of light or photons is very important for both classical optics and quantum communications. Coherent quantum interactions between light fields and matters, such as the EIT effect, are usually accompanied by light-induced refractive index changes and absorption changes [9; 111], which can be employed to actively adjust the polarization state of light under appropriate conditions. For example, through the use of quantum coherence in the Rb atomic vapor, [PERSON] et al. [112] showed that an initially isotropic atomic vapor could be modified to behave as a linearly or circularly birefringent material, which could be employed to control the polarization state of light through another controlling beam, while, through the asymmetry of the EIT effect in a multilevel system in an Rb atomic ensemble, [PERSON] et al. [113] demonstrated coherently controllable rotation of light polarization with a large tuning range. In addition, the polarization of light can also be coherently rotated based on the nonlinear magneto-optical effect under EIT conditions in Rb atomic vapor [114]. Note that all these quantum coherent controls on the light polarization were achieved in atomic vapors, which were initially isotropic. However, for solids, like Pr:YSO crystals, the situation is more complicated than atomic vapor because of the inherent birefringence and anisotropic absorptance of the crystals. We studied the EIT-induced birefringence and achieved a controllable polarization rotator at the EIT point in Pr:YSO crystal [111]. Two parameters, the orientation angle \(\varphi\) and the ellipticity \(\varepsilon\), were employed to describe the polarization state of light. Here, the orientation angle, \(\varphi\), was the crossing angle between the crystalline x-axis and the major principal axis of an elliptically polarized light, and the ellipticity \(\varepsilon\) satisfied the formula \(\tan\varepsilon=\pm b/a\), where \(a\) is half of the major axis length and \(b\) is half of the minor axis length, respectively, of the polarization ellipse, as shown in Figure 11a. In general, when a linearly polarized beam transmits through Pr:YSO crystal, the light becomes elliptically polarized due to the inherent birefringence of the crystal. When Pr:YSO crystal is in the EIT state in the simultaneous presence of the coupling and the probe beams, the polarization state of the probe light will change furthermore because of the EIT-induced birefringence. Interestingly, we found, both theoretically and experimentally, that under the exact two-photon resonant condition, the EIT-induced birefringence disappeared. This means it is possible to keep the linear polarization state of the probe light even in the presence of a strong coupling beam under the EIT condition if the inherent birefringence of the Pr:YSO crystal is compensated for in advance. Figures 11b,c show the measured frequency-detuning spectra of \(\varepsilon\) and \(\varphi\) of the transmitted probe light after the Pr:YSO crystal around the two-photon resonant point. Note that here the inherent birefringence of the Pr:YSO crystal was already compensated for in advance. It can be seen that, under the exact two-photon resonant condition, the ellipticity \(\varepsilon\) was equal to zero, while the orientation angle \(\varphi\) changed due to the resident anisotropy of absorptance. The orientation angle, \(\varphi\), can be controlled through other experimental parameters, such as the coupling beam intensity.