High-temperature photoluminescence reveals the inherent relations between quantum efficiency and emissivity

Photoluminescence (PL) is a light-matter quantum interaction associated with the chemical potential of light formulated by the Generalized Planck's law. Without knowing the inherent temperature dependence of chemical potential, the Generalized Planck's law is insufficient to characterize PL(T). Recent experiments showed that PL at low temperatures conserves the emitted photon rate, accompanied by a blue-shift and transition to thermal emission at a higher temperature. Here, we theoretically study temperature-dependent PL by including phononic interactions in a detailed balance analysis. Our solution validates recent experiments and predicts important relations, including i) An inherent relation between emissivity and the quantum efficiency of a system, ii) A universal point defined by the pump and the temperature where the emission rate is fixed to any material, iii) A new phonon-induced quenching mechanism, and iv) Thermalization of the photon spectrum. These findings are relevant to and important for all photonic fields where the temperature is dominant.