I've recently been trying to understand on a deeper level what is the physical meaning or existance of photons, and relatedly, what is the experimental verification of their existance. We all learn that historically Einstein employed them to explain the photoelectric effect, after Planck discovered the quantization of energy allows correct derivation of blackbody radiation. Later, Compton's scattering experiments were also explained successfully using the photon picture and thus it became established that EM waves somehow propagate in quanta. A few years later Dirac correctly quantized the EM field, and the resulting theory explained the quantum nature of the EM field and light propagation, explaining the photon as the minimum excitation of the EM field, and QED began. (Correct me if this is false; I'm an undergrad and still don't have a formal knowledge in QFT.)
The resulting theory also predicted verified phenomena such as the Lamb shift and the anomalous magnetic moment of the electron. However, it seems that in the years since then, many of the phenomena whose existence supposedly proves QED were derived from semiclassical models. According to Scully & Zubairy in "Quantum Optics",
"There are many processes associated with the radiation-matter interaction which can be well explained by a semiclassical theory in which the field is treated classically and the matter is treated quantum-mechanically. Examples of physical phenomena which can be explained either totally or largely by semiclassical theory include the photoelectric effect, stimulated emission, resonance flourescence.
Perhaps the most important example of a situation which is not covered by the semiclassical theory is the spontaneous emission of light. Furthermore, the Lamb shift is a good example of a physical situation which is only understood with the introduction of the vacuum into the problem... When vacuum fluctuations are included, we see that the Lamb shift is qualitatively accounted for and conceptually understood. Other phenomena, such as the Planck distribution of blackbody radiation and the linewidth of the laser, can be understood by such smiclassical plus vacuum fluctuations arguments."
Indeed as they mention, a google search shows derivations of the photoelctric effect, the compton effect, blackbody radiation, spontaneous emission, the Lamb shift, and the anomalous magnetic moment of the electron - all the classical experimental verifications for the quantization of the EM field and QED (as far as I'm aware), from semiclassical models with vacuum fluctuations.
Scully & Zubairy do go on to describe a phenomenon in which the predictions of QED and semiclassical theory differ significantly: quantum beats in $\Lambda$-type systems. In QED such systems show no quantum beats, while semiclassical theory predicts existance of beats in these systems. However, Scully & Zubairy don't mention even a single experimental verification that indeed there are no beats in $\Lambda$ systems, and I wasn't able to find any in google, either.
And so I have to ask, what is, after all, the experimental verification that indeed the EM field is also quantized (and for the existance of photons). Were there experiments trying to detect the aforementioned quantum beats? Is there another effect or phenomenon whose predictions differ between QED and semiclassical theory (with vacuum fluctuations) and was shown experimentally to follow QED behavior, and thus the EM field is definitely quantized (I found the Hong–Ou–Mandel effect which might fit here, but I don't have enough knowledge to understand whether is really shows quantization of the field)? What are the experimental verifications for the existance of photons, which cannot be explained with semiclassical theory (in which there are no photons)? Are there, perhaps, theoretical or thought-experimental arguments for this quantization, if there's no definite experimental evidence? Even though QED is a well-established and well-tested theory, I feel like this is an important question to ask, because if we don't even have clear evidence that the EM field is definitely quantized, then who is to say gravity has to be quantized...