# 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
Figure 11 shows the temperatures of 13 particles trapped using laser light at 1031 nm and 1064 nm at a pressure of 600 mbar The trapping power was 200 mW. Some changes between the temperatures of particles trapped by 1031 nm light was observed. The average internal temperature was \(\sim\) 167 K. The lowest temperature reached in this experiment was \(\sim\) 130 K. As one can see in Figure 11, in the beginning of the experiment, particle 2 was trapped using a 1031 nm laser beam. The temperature reached was 175 K. Later, the laser wavelength was changed to 1064 nm. For this wavelength, the temperature reached was 255 K (Figure 11). For this particle, the temperature was 175 K when trapped with 1031 nm light and 255 K when trapped using 1064 nm light (Figure 11). Using (6) and (7), one can show that lower temperatures can be achieved with a laser at 1020 nm. Lower pressure and improved crystal purity can also help to reach lower temperatures. Anti-Stokes cooling of Yb\({}^{3+}\)-NaYF nanocrystals was reported in [39]. A sublevel splitting of Yb\({}^{3+}\) ions doped in a NaYF host is smaller than that of Yb\({}^{3+}\) ions doped in other crystal hosts. Yb\({}^{3+}\):NaYF can provide better cooling efficiency. Yb\({}^{3+}\):NaYF particles appeared as spheres (insert in Figure 12). The fabrication process of Yb\({}^{3+}\):NaYF nanoparticles is safer than the fabrication process of Yb\({}^{3+}\):YLF nanoparticles. It is predicted that Yb\({}^{3+}\):NaYF can be cooled to \(\sim\) 5 K colder than Yb\({}^{3+}\):YLF crystals [38]. In 2021, 10% Yb\({}^{3+}\):NaLF\({}_{4}\) optically levitated nanoparticles were laser-cooled by 42 K to a temperature of 252 K [39]. The ytterbium ions were excited with a laser at 1020 nm. A 1064 nm laser was used to create an optical dipole trap. A 1064 nm laser induced a dipole in the Yb\({}^{3+}\):NaYF nanocrystal. The induced dipole moved to the point of highest  
Figure 11: Yb\({}^{3+}\):YLF crystals (inset) and their internal temperatures for 1031 nm (red) and 1064 nm (blue) trapping wavelengths. N is the particle number. Figure 12: Laser trapping and cooling Yb\({}^{3+}\):NaYF nanocrystals. A 1064 nm laser was used for the optical-dipole-trapping of Yb\({}^{3+}\):NaYF nanocrystals in a vacuum chamber. A 1020 nm laser was used for anti-Stokes laser-cooling of Yb\({}^{3+}\):NaYF nanocrystals. PBS: Polarizing Beam Splitter, DBS: Dichroic Beam Splitter, SPF: Short-Pass Filter, OSA: Optical Spectrum Analyzer. intensity of the laser field. The beam of a 1020 nm laser was collinear to the beam of the 1064 nm laser. The 1020 nm laser was responsible for anti-Stokes cooling in the system. As one can see in Figure 12, anti-Stokes photoluminescence (PL) of the trapped crystal was collected with the lens used to focus the trapping and cooling laser beams. A 1000 nm dichroic beam splitter and a 1000 nm short-pass filter permitted the separation of the PL from the laser light. The filter cut-off PL at wavelengths higher than 1000 nm (Figure 12). The collected PL was analyzed with an OSA. These spectra were used to estimate the temperature of the sample. The lowest temperatures reached by seven nanocrystals are presented in Figure 13.  
The decrease in the crystal's temperature was \(\Delta=42\) K. The lowest temperature reached was 252 K. The best decrease in the crystal's temperature \(\Delta=53\) K and the best lowest crystal's temperature 241 K were reached with one of the crystals (crystal 2). In 2021, laser cooling of 8.6 \(\pm\) 2.1 K below room temperature was observed with 10% Yb\({}^{3+}\):KLuF4 microcrystals synthesized with hydrothermal methods [40]. The experimental results achieved in laser cooling of RE-doped nanoparticles are presented in Table 1.  
Deceleration of a nanocrystal through its internal cooling was proposed in [42]. As may be seen in [43], a RE-doped nanocrystal is a charged particle. The source of its surface charge is the doping gradient. In [42], a Paul trap, which is widely used for localizing charged nanostructures, was used (Figure 14).