ABSTRACT
Cooling of solid-state matter by laser radiation has definite advantages over other types of cooling such as thermoelectric, mechanical, and fluid. Optical coolers are compact, they have no vibrations, and they use light as a coolant. Such coolers can be effectively utilized in the case of extremely small solid-state objects that are used in up-to-date optoelectronics. In the list of possible applications of laser cooling in solids there are self-cooled lasers, thermostabilized light-emitting diodes (LEDs), and space sensors. Although different solid-state materials were proposed for laser cooling in the last few decades, great success has been achieved to
date for glasses and crystals doped by the rare earth (RE) ions. There are two reasons that ensure the success of laser cooling of such materials. The first reason is a strong coupling between electrons and vibrations in the RE ion. The ion electronic structure consists of levels that are split into sublevels by a crystal field of the matrix due to the Stark effect. The energy gaps between Stark-split sublevels (SSSs) are comparable with phonon energies of the crystal matrix. So, there are conditions to observe the anti-Stokes fluorescence (ASF) in these solid systems. The second reason is the development of technology that allows producing doped materials of high purity. It means that in such RE ion systems there are low concentrations of unwanted impurities. Reducing the impurity concentrations decreases background absorption and unintended heating by a laser radiation. Laser cooling of a solid was originally attained in a Yb3+-doped fluorozirconate glass that was cooled down by 0.3°С below room temperature in 1995 [1]. Since that time, laser cooling was observed in various glasses and crystals doped by the RE ions [2-7]. At present, progress of the technology makes it possible to reach the range of cryogenic temperatures for a Yb:YLF crystal [8]. This result is better than the results obtained on cooling with the use of thermoelectric Peltier elements. The traditional model that describes the optical refrigeration of doped solids is based on a four-level system of 4f multiplet states of an RE ion [6]. In this model, the ASF is provided by (i) resonance transitions between the upper ground and lower excited levels, (ii) phonon absorption between the SSSs, and (iii) subsequent radiative relaxation to the ground states. At the same time, in such a model, the rate of the cooling cycle is very low because of the small cross section of forbidden transitions between the levels of the same ion configuration and because of the low population of the upper ground level. For improving the cooling performance in the traditional model, a nonresonant cavity for maximizing the absorbed laser power is used [6]. In the last few decades, the coherent phenomena stimulated by laser radiation, such as coherent population trapping (CPT) and electromagnetically induced transparency (EIT), have been studied in atomic physics most intensively [9]. At the same time, the CPT and EIT effects, including the room-temperature case, were demonstrated
for solid systems by several groups [10-12]. For the CPT effect to be observed, it is very important to comply with certain relations between the lifetimes of the electron levels involved in the cooling process. For example, for a Λ system, in which there exist three levels (the ground and first and upper excited levels), the presence of one metastable level with a long lifetime (the first excited level) provides optical interference phenomena. Such a situation is possible in RE-doped crystals due to the existence of dipole-allowed 4f-5d and forbidden 4f-4f optical transitions. To improve the characteristics of the cooling process, such as cooling efficiency, a minimum attainable temperature, and a cooling rate, Raman mechanisms were recently proposed [13-15]. Raman cooling used laser pulse pumping through dipole-allowed 5d ion levels by the two-photon Raman (TPR) scattering proposed for doped materials (see Section 6.4). The mechanism is based on 4f-5d and 5d-4f optical transitions involving longitudinal optical phonons of the crystal matrix. The acceleration of the cooling cycle is achieved by combining the stimulated TPR process with third pulse pumping at the allowed fluorescence transition. Nevertheless, in this model, the cooling efficiency is 0.6%. This is because of the low transition rate of the two-photon process that involves phonons. Moreover, this cooling mechanism stops working after freezing the vibrations of the optical modes. Another Raman mechanism of cooling is based on methods of coherent pumping of doped crystals [14, 15]. The coherent and complete population transfer between the ground and the first excited levels of 4f multiplet through the 5d ion levels was achieved by using the different Raman techniques, namely TPR scattering, stimulated Raman adiabatic passage (STIRAP), and the π-pulse method. It was shown in these works that the coherent pumping increases the number of electrons that participate in the cooling cycle, which leads to increasing of the cooling power. At the same time, the results showed that the deformation potential mechanism for description of the interaction between ion electrons and vibrations of the crystal medium failed to explain the establishment of the Boltzmann distribution of the electrons at the SSSs. In this chapter, we consider a cooling model with STIRAP for optical pumping of an RE-ion-doped crystal, taking into account vibronic interaction at the SSSs of ion levels. In the model, cooling
and heating processes, which make substantial contributions to the cooling mechanism, are defined. The cooling processes are attributed to the vibronic coupling of the SSSs. In addition, using vibronic interaction allows one to achieve the Boltzmann distribution of the electrons at the SSSs in a framework of the proposed model. We apply density matrix formalism for determining the time dependence of electron populations at the ion levels under the action of pulse pumping. Then, the level populations are used for estimation of cooling characteristics of the model. The calculations, which are obtained for the Yb3+:CaF2 system, show that coherent pumping by STIRAP leads to deep laser cooling of doped crystals that have technologically attainable purity to date.
