Adaptive four-level modeling of laser cooling of solids

TL;DR

This paper introduces an adaptive four-level model for laser cooling of solids that predicts cooling efficiency using minimal input data, simplifying the analysis and design of optical refrigeration systems.

Contribution

The authors extend the four-level model to include adaptive energy levels based on pumping photon energy, reducing the need for detailed absorption spectra.

Findings

Model accurately predicts cooling efficiency across materials.

Derived explicit expressions for optimal laser frequency.

Validated against experimental results for various materials.

Abstract

Laser cooling of rare-earth doped solids has been demonstrated across a wide range of material platforms, inspiring the development of simple phenomenological models such as the four-level model to elucidate the universal properties of laser cooling under various operating conditions. However, these models usually require the input of full absorption spectra that must be provided experimentally or by additional complicated atomic modeling. In this letter, we propose that a four-level model, when extended to admit effective energy levels adaptive to the pumping photon energy, can accurately predict the cooling efficiency as a function of temperature and pumping frequency using only few inputs such as the absorption coefficient measured at a single frequency and temperature. Our model exploits the quasi-equilibrium properties of the excitation of rare-earth ions for the determination of the effective four energy levels. The model is validated against published experimental results for a span of materials including ytterbium/thulium-doped glass and crystals. With the verified model, we derive explicit expressions for the optimal frequency and the operating bandwidth of pumping laser. Our model significantly simplifies the modeling process of laser cooling, and is expected to stimulate further development of optical refrigeration.