Mechanism of refrigeration cycle on laser cooling of solids

Abstract

A simple model is developed to study the laser cooling of solids. The condition of laser cooling of a solid is developed. By using some parameters of the Yb 3+ ion, which is most widely used in laser cooling, we then calculate the cooling power and the cooling efficiency. In order to make a more precise analysis, the effect of fluorescent reabsorption, which is unavoidable in the cooling process, is discussed using the random walk model. Taking Tm 3+ ion as an example, we derive the average number of absorption events and determine the change in quantum efficiency due to reabsorption. Finally, we obtain the red-shift of the fluorescent wavelength and the requirement of sample dimension.OCIS codes: 140.3320, 160.2540, 300.2530. doi: 10.3788/COL201210.031401.As early as 1929, Pringsheim proposed an idea to cool a solid material by using anti-Stokes fluorescence. In this process, the material absorbs a pumping photon with a longer wavelength and soon afterwards emits a fluorescence photon with a shorter wavelength; the energy difference between the two photons, which results from the internal energy of the material, is removed by the fluorescence radiation, and the material is cooled. Many researchers have initially opposed this idea as they cannot relate laser to refrigeration. However, in 1995, the first demonstration of net laser cooling of a solid was reported [1] , and a Yb 3+ -doped fluorozirconate glass ZBLANP was cooled to 0.3 K below room temperature. Thereafter, people have carried out a series of theoretical and experimental studies for laser cooling of solids and obtained great progress [2−12] . Since anti-Stokes fluorescence cooling has been successfully achieved, explanations about the experimental result have been continually explored. Lamouche et al. found a theoretical model [12] and derived the cooling efficiency in arbitrary temperature by evaluating the experimental spectroscopy. The relationship between the mean fluorescent wavelength and the temperature was also determined. As the model of Lamouche is very complex, we propose a simple two-level system to analyze the micro course of laser cooling and then calculate the cooling power and cooling efficiency. We then discuss several main parameters that influence cooling power and determine the relationship between temperature and time.In order to obtain efficient laser cooling of solids, the key is to choose the proper fluorescent center and its level structure, as well as the appropriate energy gap. Taking Tm 3+ ions as example, their energy manifolds are shown in Fig.