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Physics of Particles and Nuclei Letters

Superradiance regime of laser cooling in extended solids

Eugene K. Bashkirov

Published Mar 1, 2007• 0 citations
Publisher

Abstract

The kinetics of the extended crystal doped by rare-earth ions in the regime of anti-Stokes laser cooling has been considered taking into account the collective radiation effects. The system of Markovian equations for impurities and pseudolocal phonons has been obtained. As would be expected, the collective radiation effects cause an acceleration in relaxation depletion of the phonon mode and, therefore, an increase in crystal cooling efficiency.

DOI
10.1134/s1547477107020173

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The kinetics of the extended crystal doped by rare-earth ions in the regime of anti-Stokes laser cooling has been considered taking into account the collective radiation effects. The system of Markovian equations for impurities and pseudolocal phonons has been obtained. As would be expected, the collective radiation effects cause an acceleration in relaxation depletion of the phonon mode and, therefore, an increase in crystal cooling efficiency.
The method of elimination of boson operators is used to theoretically analyze the possibility and optimal conditions of superradiance regime of laser cooling of crystals and glasses doped with rare-earth ions. A set of kinetic equations governing the processes of laser cooling and optical superradiance in a multilevel system is derived for the pulsed regime. It is demonstrated that the efficiency of laser cooling in this regime is proportional to a factor N2(lambda) 2KnS, where N is the number of active impurity centers, (lambda) is the superradiance wavelength, K is the number of superradiance channels, and nS is the number of superradiance events per second.
We present a theoretical scheme for laser cooling of rare-earth-doped solids with optical superradiance (SR), which is the coherent, sharply directed spontaneous emission of photons by a system of laser-excited rare-earth ions in the solid-state host (glass or crystal). We consider an Yb+{}^{+}+-doped ZnF4{}_{4}4​-BaF2{}_{2}2​-LaF3{}_{3}3​-AlF3{}_{3}3​-NaF (ZBLAN) sample pumped at a wavelength 1015 nm, with a rectangular pulsed source with a power of \ensuremath{\sim}433 W and a duration of 10 ns. The intensity of the SR is proportional to the square of the number of excited ions. This unique feature of SR permits an increase in the rate of the cooling process in comparison with the traditional laser cooling of the rare-earth-doped solids with anti-Stokes spontaneous incoherent radiation (fluorescence). This scheme overcomes the limitation of using only low phonon energy glasses for laser cooling.
A theoretical scheme for laser cooling thulium doped solids with optical superradiance is presented. The superradiance is coherent, sharply directed spontaneous emission of photons by an ensemble of excited ions in the solid-state host, the properties of which are much different from the conventional, incoherent anti-Stokes fluorescence radiating through all directions. In this paper, we consider a thulium doped ZBLAN sample pumped with continuous-wave laser at 1.9 μm and pulse laser at 1.8 μm. The induced anti-Stokes superrandiance at 1.8 μm removes the matrical phonons energy much effectively and quickly, because of the intensity of superradiance proportional to the square of the number of excited Tm ions. The numerical evaluations of the superradiance cooling performance, especially in the net cooling power and the cooling efficiency, is discussed.