# Laser Cooling and Trapping of Rare-Earth-Doped Particles
## 3 Optical Refrigeration of Rare-Earth-Doped Particles
### Laser Cooling of Rare-Earth-Doped Mie Resonant Samples
\[\overset{\rightarrow}{M}_{o1n}^{(1)}=cos\varphi\cdot\pi_{n}(cos\theta)\cdot j _{n}(\tilde{r})\delta_{\theta}-sin\varphi\cdot\pi_{n}(cos\theta)j_{n}(\tilde{ r})\delta_{\varphi} \tag{12}\]6 System under investigation. Here, \(\lambda_{P}\) and \(\lambda_{F}\) are the pump and mean fluorescence wavelengths, respectively [29]. In [30], a nanoscale semiconductor optomechanical resonator (CdSNR) was laser-cooled with a Yb\({}^{3+}\):YLF microcrystal attached to it. The Yb\({}^{3+}\):YLF microcrystal was hydrothermally synthesized. The cooling process with a microscopic cooler provided local cooling. This approach permits a thermal steady temperature state for nanoscale devices to be achieved. A CdSNR was placed at the end of a silicon substrate. A 10% Yb\({}^{3+}\):YLF crystal was placed at the free end of the CdSNR cantilever. The 10% Yb\({}^{3+}\):YLF crystal was hydrothermally grown. The silicon substrate was located inside a cryostat chamber, which was pumped to \(\sim 10^{-4}\) torr (Figure 6). The temperature of the Yb\({}^{3+}\):YLF placed at the end of the cantilever was measured with differential luminescence thermometry (DLT) [31; 32]. Emission from different crystal-field levels of Yb\({}^{3+}\) ions was analyzed using a Boltzmann distribution. At an incident power \(P_{0}=40.1\) mW and spot radius \(w_{0}=1.15\) um, a temperature drop of 23.6 K below room temperature was observed. A cantilever of length \(L\), width \(W\), and thickness \(H\) was considered for computer simulations. The Yb\({}^{3+}\):YLF crystal of \(H_{YLF}=6\) um, \(L_{YLF}=7.5\) um, and \(W_{YLF}=6\) um was approximated as a cuboid. The volume and aspect ratio were almost the same as for the crystal used in experiments (Figure 7). The thermal conductivity of the YLF crystal \(\left(\sim 6\) Wm\({}^{-1}\)K\({}^{-1}\)\(\right)\) was relatively large. It resulted in an almost uniform temperature distribution in the crystal. \[\overset{\rightarrow}{M}_{o1n}^{(1)}=cos\varphi\cdot\pi_{n}(cos\theta)\cdot j _{n}(\tilde{r})\delta_{\theta}-sin\varphi\cdot\pi_{n}(cos\theta)j_{n}(\tilde{ r})\delta_{\varphi} \tag{12}\]7 Sample temperature, \(T_{S}\), versus the radius of the sample. Resonant radii of the nanospheres supporting MD, ED, MQ, and EQ modes are presented for simplicity of understanding [29]. \[\overset{\rightarrow}{M}_{o1n}^{(1)}=cos\varphi\cdot\pi_{n}(cos\theta)\cdot j _{n}(\tilde{r})\delta_{\theta}-sin\varphi\cdot\pi_{n}(cos\theta)j_{n}(\tilde{ r})\delta_{\varphi} \tag{12}\]8 The CdSNR cantilever supported by a silicon substrate. A Yb\({}^{3+}\):YLF crystal is placed at the free end of the cantilever [30]. As the cantilever was placed in the vacuum chamber, conduction and convection were absent. The temperature at the silicon/CdS interface (x = 0) was equal to the cryostat temperature. The authors of the paper assumed that all of the heat generated in the Yb\({}^{3+}\):YLF crystal was transferred to or from the CdSNR across the interface at \(x=L_{c}\). They calculated a cooling power for the sample with \(H=150\) nm, \(W=2.5\) mm, and \(L_{c}=53\) mm and estimated that the coldest point in the cantilever was between 26 K and 58 K below room temperature. The calculated cooling power was smaller than the experimentally obtained cooling power. The discrepancy can be explained in the following way: the size of the YLF microcrystals corresponds to the Mie scattering regime. Internal optical fields may be enhanced considerably by cavity resonances. In 2021, 10% Yb\({}^{3+}\)-doped LiLuF\({}_{4}\) (LLF) microcrystals were grown with a hydrothermal process [33]. They were transferred to electron-transparent Si\({}_{3}\)N\({}_{4}\) windows irradiated by a near-infrared laser for solid-state laser refrigeration of windows in vacuum \(\left(10^{-3}\) torr\(\right)\) (Figure 8). Analysis of the Yb\({}^{3+}\) luminescence spectrum at an irradiance of 0.854 MWcm\({}^{-2}\) revealed laser cooling by more than 20.4 K below room temperature. Using computer simulations, bulk cooling of the Si\({}_{3}\)N\({}_{4}\) window by \(\sim 15\) K was demonstrated.