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Journal of the Optical Society of America B

Vibronic model of laser cooling with stimulated Raman adiabatic passage pumping for Yb^3+-ion-doped crystals

Andrei V. Ivanov, Yu. Rozhdestvensky, E. Yu. Perlin

Published Jul 1, 2016• 13 citations
Publisher

Abstract

A vibronic model of laser cooling for crystals doped with Yb3+ ions is proposed. The model involves the stimulated Raman adiabatic passage pumping through dipole-allowed 4f–5d transitions, electron transitions between Stark-split sublevels due to vibronic interaction, and anti-Stokes fluorescence from the excited ion state. Dynamics of the cooling process are described by the density matrix formalism. It is shown that the cooling power in the case of vibronic interaction is higher at least by a factor of 3.4 compared to the case of electron–phonon interaction. In the proposed model, an increase in the cooling power yields deeper and faster refrigeration of a crystal doped with Yb3+ ions. Estimations show that, on cooling by the stimulated Raman adiabatic passage pumping, the temperature of a crystal with an irradiated volume of 2.12×10−4 cm3 can reach 64 K in a time of 2 s. In the proposed model, the cooling temperature is 30 K lower and the cooling process is 100 times faster compared to the traditional model of direct pumping. The estimates are applicable to present-day materials of technologically attainable purity.

DOI
10.1364/josab.33.001564

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A vibronic model of laser cooling for crystals doped with Yb3+ ions is proposed. The model involves the stimulated Raman adiabatic passage pumping through dipole-allowed 4f–5d transitions, electron transitions between Stark-split sublevels due to vibronic interaction, and anti-Stokes fluorescence from the excited ion state. Dynamics of the cooling process are described by the density matrix formalism. It is shown that the cooling power in the case of vibronic interaction is higher at least by a factor of 3.4 compared to the case of electron–phonon interaction. In the proposed model, an increase in the cooling power yields deeper and faster refrigeration of a crystal doped with Yb3+ ions. Estimations show that, on cooling by the stimulated Raman adiabatic passage pumping, the temperature of a crystal with an irradiated volume of 2.12×10−4 cm3 can reach 64 K in a time of 2 s. In the proposed model, the cooling temperature is 30 K lower and the cooling process is 100 times faster compared to the traditional model of direct pumping. The estimates are applicable to present-day materials of technologically attainable purity.
Methods of coherent pumping through dipole-allowed 5d levels of RE ion are proposed for laser cooling. The coherent and complete population transfer between the ground and the first excited levels of 4f multiplet is achieved by using the different Raman techniques, namely two-photon scattering, adiabatic passage method, and π-pulse pumping. It is shown that the multiplication of the number of electrons that participate in cooling cycle leads to increasing of the cooling power and to acceleration of the cooling process. The increasing of cooling efficiency of 0.5% compared to the direct pumping between 4f levels is attained through the use of dipole-allowed optical transitions. Performed estimates show that the sample temperature can achieve 94 K for current purity materials. The calculations are obtained for Yb3+:CaF2 system.
In this paper, quantum mechanical calculations of cooling characteristics for the Yb3+: YLF system with use of the vibronic model of laser cooling are presented. Dynamics of the laser cooling process for the seven-level system of an Yb ion is described by the density-matrix formalism. Dependences of the cooling characteristics on the pump intensity are obtained for various temperatures and absorption coefficients of impurity ions. It is shown that the pump intensity, at which the net cooling power has a maximum, depends on temperature. Thus, choosing the intensities, which correspond to the net cooling power maximum over the entire temperature range, we achieve a lower sample temperature at a shorter time than in the case of using a constant intensity throughout the cooling process. Calculations are performed for the parameters of the Yb3+:YLF system.
A mechanism for laser cooling of crystals doped with rare-earth ions is proposed. The mechanism involves two-photon Raman scattering through the dipole-allowed 5d ion level, electron–phonon transitions between the Stark-split sublevels, and fluorescence from the excited ion level. It is shown that, under the conditions of coherent pumping, the total population of the ground level is transferred to the excited level of the rare-earth ion, thus increasing the cooling power and accelerating the cooling process. The involvement of dipole-allowed transitions yields an increase in the cooling efficiency by 14% compared to the efficiency of direct pumping at transitions between the 4f levels. Estimations show that the temperature of the sample cooled by the proposed mechanism can reach 82.9 K for current materials with a background absorption coefficient of 4.0×10−4 cm−1.
The enhanced laser cooling performance of rare-earth-ion-doped nanocrystalline powders is predicted, compared to the bulk material, using Yb3+:Y2O3{\mathrm{Yb}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Yb3+:Y2​O3​ as the model material. This is achieved by enhancing the off-resonance, phonon-assisted absorption, which is proportional to the three factors considered in this paper: the dopant concentration, the pumping field energy, and the excitation coefficient. Using the energy transfer theory for concentration quenching, the optimum concentration corresponding to the maximum cooling power is found to be considerably larger than the currently used value, suggesting noticeable enhancement effects for laser cooling. The pumping field energy is enhanced in random nanopowders compared with bulk crystals under the same irradiation, due to the multiple scattering of photons. Photons are thus localized in the medium and do not propagate through, increasing the photon absorption of the pumping beam (and it is shown that the reabsorption of the fluorescence is negligible). Using molecular dynamics simulations, the phonon density of states (DOS) of the nanopowder is calculated, and found to have broadened modes, and extended small tails at low and high frequencies. The second-order electronic transition rate for the anti-Stokes luminescence is calculated using the Fermi golden rule, which includes the influence of this phonon DOS, and is shown to have enhancement effects on the laser cooling efficiency using nanopowders. It is finally concluded that these three enhancement mechanisms are essentially to increase the population of the three participating carriers (electron, photon, and phonon) in the interacting volume, and this also points out directions for enhancing laser cooling performance in bulk materials.
We consider a theoretical model for laser cooling with anti-Stokes fluorescence of a Yb3+:YAG sample. We have estimated the fluorescence power density removed from the system with spontaneous emission, the power density radiated with stimulated emission as well as the heat power density generated in the system by non-radiative decays from the impurities in the host material. We have investigated the influence of each of these power densities on the cooling process in Yb3+:YAG system. It has been shown how the temperature dependences of the different parameters of the system as well as the concentration of the impurities in the host influence the final temperature of the cooled sample.
A new method is analyzed for 3-D cooling of solids based on near-resonant, stimulated Raman scattering on a narrowband transition together with optical pumping on a broadband transition. Estimates of achievable cooling rates indicate that Raman cooling offers significant improvement over anti-Stkes fluorescence cooling at cryogenic temperatures and should enable the attainment of sub-Kelvin termperatures, starting from ambient conditions in bulk samples. Also the method is not restricted to ions with small Stokes shifts, and should therefore lead to diversification of the material platforms used for optical refrigeration.