Comparative Optical Spectroscopy of Er$^{3+}$, Tm$^{3+}$, and Eu$^{3+}$ Molecular Complexes at Cryogenic Temperature
Rare-earth molecular complexes are attracting increasing interest for quantum information applications because of their structural flexibility and chemical tunability. Here, we compare the cryogenic optical properties of Er$^{3+}$, Tm$^{3+}$, and Eu$^{3+}$ complexes in the same ligand environment. Optical spectroscopy shows differing behavior across the three systems: spectral hole burning is observed in the Eu$^{3+}$ complex, whereas no measurable hole is detected in the Er$^{3+}$ and Tm$^{3+}$ complexes. We measure laser-induced local heating and rethermalization in the Er$^{3+}$ and Tm$^{3+}$ powder-like samples, observing strong local heating and slow thermal relaxation in the cold-plate cryostat. The recovery occurs over several seconds and, for some Er$^{3+}$ excitation conditions, extends over tens of seconds. The comparison across the three ions nevertheless suggests that heating alone is unlikely to account for the full contrast. Rather, the different behaviors of Eu$^{3+}$, Tm$^{3+}$, and Er$^{3+}$ point to ion-dependent relaxation and decoherence processes associated with their electronic level structure and coupling to the molecular environment. Temperature-dependent linewidth and line-shift measurements are further consistent with phonon-mediated broadening through coupling to crystal-field levels.