Temperature dependence of optical linewidths and specific heat of rare-earth-doped silicate glasses

Optical dephasing and specific heat measurements were performed on two rare-earth-doped silicate glasses. The effective homogeneous linewidth of the optical transition, ${\mathrm{\Gamma }}_{\mathrm{hom}}$ was compared to the two-level-system (TLS) contribution to the specific heat, ${\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}$, between 0.4 and 12 K. Both ${\mathrm{\Gamma }}_{\mathrm{hom}}$ and ${\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}$ vary as ${\mathit{T}}^{\mathrm{\alpha }}$ with the same value of α for a given rare-earth/glass sample, but with different α for the two samples (α=1.3 for the ${\mathrm{Pr}}^{3+}$/glass, α=1.0 for ${\mathrm{Eu}}^{3+}$/glass). From the ratio of ${\mathrm{\Gamma }}_{\mathrm{hom}}$ to ${\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}$ for each glass, it appears that the coupling strengths to the TLS for each rare-earth optical transition are similar, but that the density of TLS differ due to their different compositions.