Vibrational dynamics of isolated hydrogen in germanium

Absorption line shapes associated with the stretch mode of bond-center hydrogen $\left({\mathrm{H}}_{\mathrm{BC}}^{\mathrm{}(+)\mathrm{}}\right)$ at $1794{\mathrm{cm}}^{-1}$ and the twofold degenerate mode of hydrogen near the tetrahedral site $\left({\mathrm{H}}^{\left(-\right)}\right)$ at $745{\mathrm{cm}}^{-1}$ in germanium are measured with infrared-absorption spectroscopy. The ${\mathrm{H}}_{\mathrm{BC}}^{\mathrm{}(+)\mathrm{}}$ line shape measured at 10 K for the case of low hydrogen concentrations gives a lifetime between 15 and 23 ps. Similar in magnitude to the $7.8\pm 0.2\mathrm{ps}$ observed for the same defect in silicon [M. Budde et al, Phys. Rev. Lett. $85,$ 1452 (2000)], this observation indicates that the lifetime of the bond-centered mode is largely insensitive to the phonon frequency distributions of the host material. Pure dephasing dynamics of hydrogen in germanium are studied by measuring the shape of the 1794- and $745-{\mathrm{cm}}^{-1}$ lines as a function of temperature. These measurements are analyzed using a recently formulated exchange model for vibrational dephasing. The temperature dependence of the $1794-{\mathrm{cm}}^{-1}$ line shape is attributed to thermal fluctuations in the occupation number of a pseudolocalized mode at $75\pm 2{\mathrm{cm}}^{-1}.$