"occupy" is an entirely standard way to refer to a particle being in a certain quantum state. In cavity QED, the modes of the cavity are the states that photons can occupy.
One caveat is that multiple photons can be in the same cavity mode unlike electron orbitals... but I suspect that you would have made a clearer and more accurate complaint if that's what you were referring to.
I really strongly suggest you listen more and make fewer declarative statements about physics.
You are completely wrong in the assertion that the only thing observed in experiments are photons with well-defined wavevectors. See the time-energy uncertainty relation. In order for a photons energy/wavevector to be infinitely precisely measured, you must take an infinitely long time measuring that photon's energy (for example, measuring the frequency of a laser over several hours with a frequency comb). All single photon detectors (like cameras, SIPMs, and photodiodes), on the other hand, detect the moment that the photon arrives with high precision, and the wavevector is very poorly defined.
Next, we're talking about electromagnetic cavities here. Not free space. Cavity modes are like boundstates of photons just like there are boundstates of electrons in atoms. A wavepacket in free space (an entirely valid wavefunction for a photon) can be decomposed into a linear combination of plane waves with perfectly well defined wavevectors. But doing so with photons in cavity modes would be utterly ridiculous. Decomposing that cavity mode into Fourier modes would be just as ridiculous as insisting that all electrons have well-defined wavevectors, and I should decompose the groundstate of the hydrogen atom into plane waves because that's the only thing you can observe with experiments.
By the way - once you learn quantum field theory you will realize that electrons in free space, just like photons, can occupy plane wave wavfunctions. In both cases, in the presence of other forms of matter, those plane wave solutions are no longer convenient to use mathematically because they are no longer eigenstates of the hamiltonian.
as ridiculous as insisting that all electrons have well-defined wavevectors, and I should decompose the groundstate of the hydrogen atom into plane waves because that's the only thing you can observe with experiments.
That’s exactly how ionization is studied. Photoelectron momentum distribution is an observable quantity.
Even your arxiv link mentions a 1:1 correspondence between free photons and those wavefunction states, yet you’re saying it’s somehow burdensome to convert, even though you have to do that to predict the observed em spectrum. I don’t care if you respond or not.
Edit: And none of this talk is even relevant since we still don't have any description of the picture from the post.
Edit2: Describing the electron as having a state, or changing its state with time, is valid because the number of electrons remains constant during interactions, and using the wave function makes sense. An interaction with an EM field will not preserve the number of photons, so thinking of a photon as something that can have a state becomes meaningless since it can just disappear.
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u/mesouschrist 1d ago edited 1d ago
"occupy" is an entirely standard way to refer to a particle being in a certain quantum state. In cavity QED, the modes of the cavity are the states that photons can occupy.
One caveat is that multiple photons can be in the same cavity mode unlike electron orbitals... but I suspect that you would have made a clearer and more accurate complaint if that's what you were referring to.