I know that we explain the slowing down of light in a dispersive medium classically, by inducing small dipoles in the medium (which holds as long as being far away from absorption bands), and the induced dipoles re-emit radiation of the same wavelength but different phase, as being delayed, which ends up in slowing down of the phase velocity:


However, the group velocity can be faster than $c$ in special dispersive media (fast light). I was reading a pretty nice explanation here https://www.photonics.com/Articles/Fast_Light_Slow_Light_and_Optical_Precursors/a27833. However, the explanation for the group velocity is a bit like information is encoded in a radio signal. Each single wavelength the group consists of, is affected differently by dispersion, and in the end this signal modulation is transmitted faster than $c$. The cited article then points out that special relativity (no info faster than light) is still true, because it can be shown that the front velocity is always $c$ (not $\frac{c}{n}$), so that's the maximum speed information can be transferred (leaving the group velocity being faster than $c$ somehow an apparent effect).

The provided intuitive explanation in the article cited above, is said to be going back to Sommerfeld himself: "When the electromagnetic field first starts to interact with the oscillators, the oscillators cannot immediately act back on the field via the induced polarization, because they have a finite response time. Thus, for a brief moment after the front passes, the dispersive material behaves as if there is nothing there — as if it were vacuum".

And that leaves me wondering what happens if we only emit a single photon. There is no group just one photon. Will it be slowed down and propagate by the phase velocity, because of inducing dipoles acting back on its wave-nature? I always thought so, but after reading the article I tend to think a single photon is always a front and will propagate with the front velocity.

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    $\begingroup$ Use wave models for wave phenomena, particle models for particle phenomena. Phase and group velocity are wave phenomena. $\endgroup$
    – John Doty
    Jul 26, 2022 at 21:51
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    $\begingroup$ @John Doty I see... but then what's front velocity, a wave or particle phenomenon? And if it's wave as well... what is then the speed of a photon as a particle in a dispersive medium (I could ask the probability for a photon hitting an atom 3 km inside a glass plate - I guess I will need the photon's speed for that, plus treating it as a particle). $\endgroup$ Jul 26, 2022 at 22:14
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    $\begingroup$ What we see in experiments is that the probability of an atom absorbing a photon is proportional to the squared amplitude of the electromagnetic wave at its location. You may model the propagation of the energy as a wave. The photon may show up anywhere the wave goes. Until you detect it, it has no more reality than that. $\endgroup$
    – John Doty
    Jul 26, 2022 at 22:53
  • $\begingroup$ see this single photon at a time experiment described here physics.stackexchange.com/q/285142. The wave nature appears only in the accumulation, each photon has a path that is different in length , but it is not slowed down, always the velocity is c. $\endgroup$
    – anna v
    Jul 27, 2022 at 3:31


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