Experimental demonstration of multiphonon-assisted anti-Stokes and Stokes excitation of rare-earth ions (
R3+) in different hosts, that is, in a weak-coupling ion-lattice interaction case, is obtained. An exponential behavior of excitation probabilities with respect to energy difference between excitation and electronic line is found, just as for multiphonon-assisted nonradiative decay and energy transfer. Exponential parameters ${\ensuremath{\alpha}}_{\mathrm{AS}}$ and ${\ensuremath{\alpha}}_{\mathrm{S}}$ for anti-Stokes and Stokes excitation are measured and linked to the Miyakawa-Dexter $\ensuremath{\alpha}$ parameter for decay, leading to estimates for Pekar-Huang-Rhys coupling parameter
S0 of about 0.04, in agreement with values obtained from one-phonon spectra or nonradiative-decay measurements. A semiempirical formula is deduced to obtain $\ensuremath{\alpha}$ from only one parameter, an effective phonon energy.
This review focuses on optical refrigeration with the anti-Stokes fluorescence of rare-earth (RE)-doped low-phonon micro- and nanocrystals. Contrary to bulk samples, where the thermal energy is contained in internal vibrational modes (phonons), the thermal energy of nanoparticles is contained in both the translational motion and internal vibrational (phonons) modes of the sample. Much theoretical and experimental research is currently devoted to the laser cooling of nanoparticles. In the majority of the related work, only the translational energy of the particles has been suppressed. In this review, the latest achievements in hybrid optical refrigeration of RE-doped low-phonon micro- and nanoparticles are presented. Hybrid cooling permits the suppression of not only the translational energy of the RE-doped particles, but also their internal vibrational phonon thermal energy. Laser cooling of nanoparticles is not a simple task. Mie resonances can be used to enhance laser cooling with the anti-Stokes fluorescence of nanoparticles made of low-phonon RE-doped solids. Laser-cooled nanoparticles is a promising tool for fundamental quantum-mechanical studies, nonequilibrium thermodynamics, and precision measurements of forces.