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This was discussed in an answer to a related question but I think that it deserves a separate and, hopefully, more clear answer.

Consider a single photon ($\lambda$=532 nm) traveling through a plate of perfect glass with a refractive index $n=1.5$. We know that it does not change its direction or other characteristics in any particular way and propagating 1 cm through such glass is equivalent to 1.5 cm of vacuum. Apparently, the photon interacts with glass, but what is the physical nature of this interaction?

Let's not consider high-order effects like Rayleigh/Raman scattering.

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I realized that what I said in my last comment there wasn't really correct. So it's good that you brought this up. I am looking forward to the answers. – Marek Dec 14 '10 at 20:14
I'm not sure that the assumption that a photon travels in a straight line at lower speed is correct. I don't know enough quantum mechanics to provide that answer. I could provide a completely classical answer, though. That would discuss the glass as a dielectric. However, this would not talk about a single photon. It would talk about an electromagnetic plane wave (which does move in a straight line at lower speed). My understanding is that any single photon would be absorbed and re-emitted, effectively traveling at the full speed of light in a non-straight path. – Mark Eichenlaub Dec 14 '10 at 20:40
@Mark: the answer that my professor gave was actually similar when I asked him this question some months ago. He said that it was quite easy to explain via wave-mechanics but explaining via photon interactions was a bit tricky. He mainly stated that photons get absorbed, then emitted at the exact same wavelength, and possibly mostly due to conservation of momentum, most of the photons continue their initial path. – Cem Dec 14 '10 at 21:18
up vote 21 down vote accepted

This is a tricky question to answer, because in many ways it doesn't make sense to talk about a definite path followed by a single photon. Quantum mechanics is inherently probabilistic, so all we can really talk about are the probabilities of various outcomes over many repeated experiments with identically prepared initial states. All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other.

The transmission of light through a medium is easier to explain in a classical sense, where you think of the light beam as a wave that drives oscillations in the atomic dipoles making up the material. Each atom then re-radiates its own waves at the same frequency, but slightly out of phase. The sum of the initial wave and the re-radiated wave is a wave that lags behind the incoming wave a little bit, which explains the reduced speed. A beam of light entering a block of material tends to continue in the same direction because forward scattered light from any individual atom tends to interfere constructively with forward scattered light from other atoms in the material, while light scattered off to the sides mostly interferes destructively, and cancels out.

Carrying this picture over to the quantum regime, you would say that a single photon entering the material will potentially be absorbed and re-emitted by each of the atoms making up the first layer of the material. Since we cannot directly measure which atom did the absorbing, though, we treat the situation mathematically as a superposition of all the possible outcomes, namely, each of the atoms absorbing then re-emitting the photon. Then, when we come to the next layer of the material, we first need to add up all the wavefunctions corresponding to all the possible absorptions and re-emissions, and when we do that, we find that just as in the classical wave case, the most likely result is for the photon to continue on in the same direction it was originally headed. Then we repeat the process for all the atoms in the second layer, and the third, and so on.

At any given layer, the probability of being absorbed then re-emitted by any individual atom is pretty tiny, but there are vast numbers of atoms in a typical solid, so the odds are that the photon will be absorbed and re-emitted during the passage through the glass are very good. Thus, on average, the photon will be delayed relative to one that passes through an equal length of vacuum, giving rise to the lower observed transmission velocity.

Of course, it's not possible to observe the exact path taken by any photon-- that is, which specific atoms it scattered from-- and if we attempted to make such a measurement, it would change the path of the photon to such a degree as to be completely useless. Thus, when we talk about the transmission of a single photon through a refractive material, we assign the photon a velocity that is the average velocity determined from many realizations of the single photon experiment, and go from there.

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Your explanation is fine, but I think it should be stressed even stronger that slowing down is a collective effect, whichever view you take, classical or quantum. It means, in particular, that the simplistic quantum description (when a photon is absorbed and then re-emitted by any given atom) is misleading. The photon scatters off all atoms simultaneously, with appropriate phase shifts, and it is the interference of all such processes together with the original wave that looks like slowing down. You did say it, but I feel like this key idea is lost in the middle of your text. – Igor Ivanov Dec 14 '10 at 23:21
Yeah, that's worth emphasizing. The slowing effect is really due to the distributed, wavelike part of the photon behavior (or the fact that the photon is an excitation of an extended mode of the EM field, if you want to put it in that language), and the collective effect of all the possible scattering paths. – Chad Orzel Dec 15 '10 at 1:04
In classical case the observed photon's momentum in matter is $n$ times larger that in vacuum. Does it make sense in quantum theory? – gigacyan Dec 15 '10 at 12:47
The question of what the photon momentum is inside a material with a refractive index n is a complicated and subtle one. You can construct sensible arguments that it should be n times greater than in vacuum, and also that it should be n times smaller. There have also been experiments consistent with each. A few years ago, there was a paper that claimed to resolve this by showing that each is valid in a particular regime, but I can't find it right now. – Chad Orzel Dec 15 '10 at 14:44
There was a paper just a few month ago: Stephen M. Barnett, Resolution of the Abraham-Minkowski Dilemma, Phys. Rev. Lett. 104, 070401 (2010). – Igor Ivanov Dec 15 '10 at 20:22

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