# Laser Cooling and Trapping of Rare-Earth-Doped Particles
## 3 Optical Refrigeration of Rare-Earth-Doped Particles
### Laser Trapping and Cooling Rare-Earth-Doped Particles  
Consider RE-doped particles under both translational and internal laser cooling. Currently available methods for nanoparticle cooling allow translational temperatures of a few hundred microkelvin to be achieved [35]. Consider new mechanisms of optical cooling that allow us to reduce the translational temperature of a sample concurrently with its internal cooling, which tends to decrease the internal temperature of the sample. Here, 10% Yb\({}^{3+}\)-doped \(\beta\)-NaYF\({}_{4}\) nanowires in a fluid medium (D\({}_{2}\)O) were laser-trapped and cooled with a near-infrared single-beam at the wavelength 1020 nm (inset in Figure 9) [36]. \(\beta\)-NaYF\({}_{4}\) nanowires were prepared using a low-cost, scalable hydrothermal synthesis [37]. A nanowire can be considered as a cylinder (height \(\sim\) 2000 nm) with an hexagonal cross-section (edge \(\sim\) 255 nm). As one can see in Figure 9a, undoped (0% Yb\({}^{3+}\)) \(\beta\)-NaYF\({}_{4}\) nanowires under identical conditions (an irradiance of 73 MWcm\({}^{-2}\) at the pump wavelength 1020 nm) undergo heating by 6 \({}^{\circ}\)C above the ambient temperature. Figure 8: Schematic of 10% Yb\({}^{3+}\):LLF microcrystals placed on a Si\({}_{3}\)N\({}_{4}\) TEM window. Figure 7: The geometry of the system [30]. In [38], a similar approach based on single-beam laser trapping at the wavelength 1020 nm was used for optical refrigeration of Yb\({}^{3+}\):YLF nanocrystals (Figure 10a) prepared using the same method as in [36]: low-cost, scalable hydrothermal synthesis [37]. Using cold Brownian motion analysis, the temperature of an Yb\({}^{3+}\):YLF nanocrystal in a fluid medium (D\({}_{2}\)O) was estimated for different irradiances (Figure 10b). As one can see in Figure 10b, trapping at the wavelength 1064 nm gives rise to heating of a sample. The wavelength \(\lambda_{p}=1064\) nm is energetically insufficient to be absorbed by Yb\({}^{3+}\) ions and subsequently cannot initiate upconversion laser cooling. At the trapping wavelength of 1020 nm, 10%Yb\({}^{3+}\):YLF crystals were observed to cool from 19 \({}^{\circ}\)C at a 5.9 MWcm\({}^{-2}\) trapping irradiance to 4 \({}^{\circ}\)C at a 25.5 MWcm\({}^{-2}\) trapping irradiance (Figure 10b). In the cases being considered, laser refrigeration of RE-doped particles has been demonstrated in optical tweezers in liquid. It was analyzed by measuring cold Brownian motion. Consider optical refrigeration of RE-doped levitated particles optically trapped in a low-pressure environment. The ability to arrange levitated particles in vacuum is a promising instrument for understanding macroscopic quantum mechanics [32]. The changes in fluorescence of the nanocrystal as a function of laser trap wavelength were used to measure the temperature of the particle. Indeed, fluorescence spectra are directly related to the relative populations of sublevels of the excited \({}^{2}F_{5/2}\) manifold via the Boltzmann distribution. The changes in the damping of the motion of the nanocrystal with the temperature were also used for temperature measurements. When the optically refrigerated particle is levitated in gas, cooling of the gas molecules surrounding the particle takes place in the system. A modification in the local gas viscosity  
Figure 10: Laser cooling of laser-trapped Yb\({}^{3+}\):YLF microcrystals. (**a**) Optical micrograph of a laser-trapped Yb\({}^{3+}\):YLF crystal. (**b**) Temperature of laser-trapped particles in D\({}_{2}\)O as determined using the cold Brownian motion analysis [38]. Figure 9: Temperature of individually trapped \(\beta\)-NaYF\({}_{4}\) nanowires under 1020 nm laser irradiance: (**a**) undoped samples (0% Yb\({}^{3+}\):NaYF\({}_{4}\)) and (**b**) 10% Yb\({}^{3+}\):NaYF\({}_{4}\) samples. also takes place in the system. The damping rate of the translational motion of a particle undergoes changes as a result of hot or cold Brownian motion of the particle. The effect was used to measure particle temperature.