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The remarkable physical properties of buckminsterfullerene, C$_{60}$, haveattracted intense research activity since its original discovery. Total quantumstate resolved measurements of isolated C$_{60}$ molecules have been ofparticularly long-standing interest. However, such observations have to datebeen unsuccessful due to the difficulty in preparing cold, gas-phase C$_{60}$in sufficiently high densities. Here we report high resolution infraredabsorption spectroscopy of C$_{60}$ in the 8.5 $\mu$m spectral region. Acombination of cryogenic buffer gas cooling and cavity-enhanced directfrequency comb spectroscopy has enabled the observation of quantum stateresolved rovibrational transitions. Characteristic nuclear spin statisticalintensity patterns provide striking confirmation of the indistinguishability ofthe sixty $^{12}$C atoms, while rovibrational fine structure encodes furtherdetails of the molecule's rare icosahedral symmetry. These observationsestablish new possibilities in the study and control of emergent complexity infinite-sized quantum systems such as fullerenes.

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