Evidence for long-range interactions between rare-earth impurity ions in nanocrystals embedded in amorphous matrices with the two-level systems of the matrix

The low-temperature homogeneous broadening of the electronic transitions of ${\mathrm{Eu}}^{3+}$ and ${\mathrm{Pr}}^{3+}$ rare-earth impurity ions in ${\mathrm{Y}}_2{\mathrm{O}}_3$ and ${\mathrm{LaF}}_3$ nanocrystals embedded into amorphous materials (polymer and oxyfluoride glass ceramics) was studied with hole-burning and fluorescence line narrowing techniques. It is shown that the homogeneous linewidth is determined by the interaction of the impurity ions contained in the nanocrystals with the two-level systems (TLS’s) of the surrounding glass matrix. A comparison of the experiments with a calculation provides direct evidence for the long-range nature of the interaction with the TLS’s.