Rotor in a Cage: Infrared Spectroscopy of an Endohedral Hydrogen-Fullerene Complex*

We report the observation of quantized translational and rotational motion of molecular hydrogen inside the cages of C$_{60}$. Narrow infrared absorption lines at the temperature of 6\,K correspond to vibrational excitations in combination with translational and rotational excitations and show well-resolved splittings due to the coupling between translational and rotational modes of the endohedral H$_2$ molecule. A theoretical model shows that H$_2$ inside C$_{60}$ is a three-dimensional quantum rotor moving in a nearly spherical potential. The theory provides both the frequencies and the intensities of the observed infrared transitions. Good agreement with the experimental results is obtained by fitting a small number of empirical parameters to describe the confining potential, as well as the {\it ortho\/} to {\it para\/} ratio at 6\,K and at elevated temperatures [S. Mamone, et al., arXiv:0807.1589v2].