Anharmonic vibrational relaxation dynamics for a molecular impurity mode in alkali halide crystals

High-resolution diode-laser spectroscopy and the nonequilibrium techniques of incoherent laser saturation and transient hole-burning spectroscopy have been used to measure the relaxation dynamics (specifically $T_1$ and $T_2$) of the ${\nu }_3$ internal vibrational mode of Re$\mathrm{O}_4^{}{}_{}{}^{-}$ molecules as functions of temperature and host alkali halide lattice. Inhomogeneously broadened linewidths less than 0.02 ${\mathrm{cm}}^{-1\mathrm{}}$ were observed in annealed crystals at low temperatures. To retrieve the homogeneous linewidths from the inhomogeneously broadened lines, hole-burning measurements of $T_2$ were performed with the use of a C${\mathrm{O}}_2$ laser as a saturating pump and either a Pb-salt diode laser or another C${\mathrm{O}}_2$ laser as a tunable probe. Holes as narrow as 10 MHz (full width at half maximum) were observed in inhomogeneously broadened lines several ${\mathrm{cm}}^{-1\mathrm{}}$ wide. Excited-state lifetimes $T_1$ were measured by C${\mathrm{O}}_2$-laser saturation measurements, which provide values for the saturation intensity $I_s$ and hence the product $T_1{T}_2$. Above 10 K the dominant dephasing ($T_2$) mechanism is acousticphonon scattering, whereas below 10 K $T_2$ achieves the fundamental upper limit of ${2T}_1$, signifying that dephasing is lifetime limited. The results of a systematic study of the alkali halide host lattice dependence of the excited-state decay rate at low temperatures show that the decay channel consists of multistep emission of lower-energy internal modes, localized phonon modes, and band phonons.