Recently, rotational spectra of giant Rydberg matter (RM) clusters were studied in the radio frequency range (Mol. Phys. 105 (2007) 933-939), giving high-precision bond distances in the nanometer range. However, the theoretical and experimental problem of vibrational motion or, rather, coupled electronicvibrational motion in the RM clusters is still unsolved; but it is expected that broad phonon bands will exist. Spectroscopic signatures from space make it likely that RM is a common form of matter in the Universe, and phonon bands in this spectroscopic range have not been taken into account so far. Spectroscopic results are now reported on transitions in the range 0.01-20 cm −1 , using primarily infrared (IR) lasers to probe the RM in a tunable open cavity with a Fabry-Perot interferometer to aid in the identification of the shifts. Stimulated Raman scattering from electronic transitions and Rabi-flopping from electronic states in the clusters are observed. The broad stimulated Raman peaks are assigned to one and two consecutive vibrational (electronic-vibrational) transitions. Theoretical values predicted for vibrations (phonon maxima) and electronic processes are in reasonable agreement with the experimental results. Improved calculations are needed to verify the assignments of the vibrational phonon distributions.