Quantum state resolution of the C$_{60}$ fullerene

The remarkable physical properties of buckminsterfullerene, C$_{60}$, have attracted intense research activity since its original discovery. Total quantum state resolved measurements of isolated C$_{60}$ molecules have been of particularly long-standing interest. However, such observations have to date been unsuccessful due to the difficulty in preparing cold, gas-phase C$_{60}$ in sufficiently high densities. Here we report high resolution infrared absorption spectroscopy of C$_{60}$ in the 8.5 $\mu$m spectral region. A combination of cryogenic buffer gas cooling and cavity-enhanced direct frequency comb spectroscopy has enabled the observation of quantum state resolved rovibrational transitions. Characteristic nuclear spin statistical intensity patterns provide striking confirmation of the indistinguishability of the sixty $^{12}$C atoms, while rovibrational fine structure encodes further details of the molecule's rare icosahedral symmetry. These observations establish new possibilities in the study and control of emergent complexity in finite-sized quantum systems such as fullerenes.