# Accurate Characterization of the Properties of the Rare-Earth-Doped Crystal for Laser Cooling
## 4 Results and Discussions  
Under the irradiation of the 1015 nm pump laser, the 5% Yb\({}^{3+}\)-doped LuLiF\({}_{4}\) crystal is optically cooled. With the decrease in the sample temperature the pixel intensities of thermal images are reduced, as shown in Figure 4a. The sample temperature reaches a steady state after 20 min of irradiation. The averaged pixel intensities decrease from 158 to 102.1, corresponding to a pixel intensity drop of 55.9 and a sample temperature drop of about 4.3 K. When the pump wavelength is changed to 1080 nm, the 5% Yb\({}^{3+}\)-doped LuLiF\({}_{4}\) crystal is optically heated. The sample reaches a steady state in temperature after 20 min of irradiation. With the increase in the sample temperature, the pixel intensities of thermal images are enhanced, as shown in Figure 4b. The averaged pixel intensities increase from 161.8 to 206, corresponding to a pixel intensity rise of 44.2 and a sample temperature rise of about 3.4 K.  
Figure 3: The calibration of the thermal camera. (**a**) The side view of the thermal image of the CGTC through the BaF\({}_{2}\) windows. The red dash area on the surface of the sample is used for calculating the average pixel intensity. (**b**) The variation in the reference crystal temperature with TEC current for three cases. (**c**) Calibrating the relationship between the pixel values of the sample thermal image and its temperature. (**d**) The relationship between the pixel value changes of the sample thermal image and its temperature. Similar experimental studies were also performed in other pump wavelengths in the range of 1010 nm and 1080 nm. The temperature changes of the crystal at each pump wavelength were extracted from thermal images following the above-mentioned image-processing procedure, which involves both spatial and temporal averaging. The CGTC temperature was kept at a constant value of 22 \({}^{\circ}\)C during the experiment. The absorbed power \(P_{abs}(\lambda)\propto k\int S(\lambda)d\lambda\) at each pump wavelength \(\lambda\) was calculated from the photoluminescence excitation spectroscopy measurement technique. The measured cooling efficiency \(\eta_{c}(\lambda)^{exp}\) for each pump wavelength was fitted with Equation (1). The corresponding results are shown in Figure 4c. The external quantum efficiency \(\eta_{ext}=99.4(\pm 0.1)\%\) and the background absorption coefficient \(\alpha_{b}=1.5(\pm 0.1)\times 10^{-4}\) cm\({}^{-1}\) are acquired accordingly. The net cooling of the sample is observed between the first zero-crossing wavelength \(\lambda_{cross1}\) = 1005 nm and the second crossing wavelength \(\lambda_{cross2}\) = 1065 nm. The filled blue region between \(\lambda_{cross1}\) and \(\lambda_{cross2}\) represents the cooling area. A \"cooling window\" capable of predicting the optical cooling potential of the sample can be calculated according to the cooling parameters of the crystal, such as \(\eta_{ext}\), \(\alpha_{b}\), \(\alpha_{r}\) and \(\lambda_{f}\) measured in experiment. Figure 4d shows the \"cooling window\" of the 5% Yb\({}^{3+}\):LuLiF\({}_{4}\) crystal under our study. The dash line separating the blue area of cooling and red area of heating indicates the points where the cooling efficiency is equal to zero. From Figure 4d one can see that the global MAT of the crystal can reach \(\sim\)110 K at 1020 nm by maximizing the power absorption of the pump laser (astigmatic Herriot cavity [55; 56]) and minimizing heat loads from the environment [46; 49; 50]. The cooling performance of a sample strongly depends on its cooling parameters, such as \(\eta_{ext}\) and \(\alpha_{b}\) etc. In a previous work, a temperature drop of \(\sim\)2.2 K was reported in a  
Figure 4: The LITMoS test of the 5% Yb\({}^{3+}\):LuLiF\({}_{4}\) crystal. (**a**) The pixel intensity changes of the thermal camera at 1015 nm pumping. The inset is the thermal image of the sample. (**b**) The pixel intensity changes of the thermal camera at 1080 nm pumping. The inset is the thermal image of the sample.