Thermodynamic constraints on photoluminescent cooling with coherent and incoherent light sources

Cooling solids with anti-Stokes photoluminescence, involving the emission of photons with higher energy than incident photons, has been demonstrated in various materials, such as rare-earth-doped glasses. Requiring that the increase in entropy of radiation must be higher than the decrease in entropy of the sample imposes constraints on the efficiency of the cooling process. We study the role of the properties of the light source, such as coherence, unidirectionality, and monochromaticity, in optical cooling. We use the most general formulation of radiation entropy in terms of the von Neumann entropy of the photon field, which allows us to study a variety of light sources. We show that as long as the incident radiation is unidirectional, the loss of coherence does not significantly affect the cooling efficiency. Our results suggest that the laws of thermodynamics allow us to optically cool materials with incoherent sources like LEDs and filtered sunlight almost as efficiently as with lasers.