The energy of an atom binding one photon in a cavity can be derived classically. But when two photons are bound to the atom, signatures of light quantization appear in the spectrum. These have now been observed in the optical domain.
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Carmichael, H. Signs of anharmonicity. Nature Phys 4, 346–347 (2008). https://doi.org/10.1038/nphys953
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DOI: https://doi.org/10.1038/nphys953
