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Transient photoluminescence enhancement as a probe of the structure of impurity-trapped excitons in CaF$_2$:Yb$^{2+}$

We demonstrate a direct measurement of the energy levels of impurity-trapped excitons in CaF$_2$:Yb$^{2+}$. The radically different radiative decay rates of the lowest exciton state and higher excited states enable the generation of a transient photoluminescence enhancement measured via a two-step excitation process. We observe sharp transitions arising from changes of state of localized electrons, broad bands associated with changes of state of delocalized electrons, and broad bands arising from trap liberation.