The speed of one photon through a transparent medium

[isotherm]

TL;DR Summary

I want to learn if the speed of one photon in a transparent medium is c/n or not and, of course, why.

We know from double-slit experiments that singular photons behave like waves, so I expect that one photon would undergo refraction when entering, with an angle different than 90 degree, into water, glass or other transparent material. Is that true?

If the refraction occurs, than the speed of singular photons though the transparent material is c/n? If this is true, how it is explained? I ask this because the explanation from wikipedia with the charges in the material "shaken" back and forth and radiating their own electromagnetic wave doesn't sound right. I don't see how from one photon you can obtain more (their own electromagnetic wave). If it is correct, we may use it to produce energy

So, what is the speed of one photon through a transparent medium and why?

 

[PeterDonis]

"One photon" is not what you think. The concept of "speed" does not even make sense for one photon. Nor does the concept of having a definite path through space, which is what you would need for "refraction" to make sense. Nor does the concept of "electromagnetic wave". (The "waves" that explain interference in the double slit experiment for single photons are quantum waves, which are not the same thing as the "electromagnetic wave" that appears in Wikipedia's explanation.)

In short, none of your questions are even well defined for "one photon".

 

[PeroK]

TL;DR Summary: I want to learn if the speed of one photon in a transparent medium is c/n or not and, of course, why.

We know from double-slit experiments that singular photons behave like waves, so I expect that one photon would undergo refraction when entering, with an angle different than 90 degree, into water, glass or other transparent material. Is that true?

If the refraction occurs, than the speed of singular photons though the transparent material is c/n? If this is true, how it is explained? I ask this because the explanation from wikipedia with the charges in the material "shaken" back and forth and radiating their own electromagnetic wave doesn't sound right. I don't see how from one photon you can obtain more (their own electromagnetic wave). If it is correct, we may use it to produce energy

So, what is the speed of one photon through a transparent medium and why?

The photon is, technically, the quantum of the quantized EM field. And a single photon is a particular state of the EM field. Feynman's book "The Strange Theory of Light and Matter" gives a basic QM description of the phenomena of reflection, refraction and diffraction.

There are no photons in classical EM, where light is modelled as an EM wave obeying Maxwell's equations. It's a common misconception to confuse the two theories of light. It doesn't make any sense to try to apply the classical explanation in Wikipedia to a photon.

 

[Dale]

As @PeterDonis and @PeroK said, your question actually is quite problematic. A lot of the things you like to think about for massive classical particles don’t apply for massless quantum particles. At least, not without a lot of caveats.

However, if you have a single photon source of optical photons, and you send them through a lens one at a time, then the density of photon detections will be very high at exactly the same place that classical light will focus.

Make what you will of that. To me it is a “yes with lots of aforementioned caveats”

 

[Vanadium 50]

You can have source emitting a photon at a certain place and time (sort of). You can have detector receiving a photon at a certain place and time (again, sort of). But there is no way to say these are the same photon, much less say anything about a path from source to detector.

 

[isotherm]

The concept of "speed" does not even make sense for one photon.

If I search "speed of photon" I get:

Photons are massless, so they always move at the speed of light when in vacuum, 299792458 m/s

It is true? And "always" means also in a medium?

 

[isotherm]

The "waves" that explain interference in the double slit experiment for single photons are quantum waves, which are not the same thing as the "electromagnetic wave" that appears in Wikipedia's explanation.

Ok.

It doesn't make any sense to try to apply the classical explanation in Wikipedia to a photon.

Ok, thank you.

 

[isotherm]

You can have source emitting a photon at a certain place and time (sort of). You can have detector receiving a photon at a certain place and time (again, sort of). But there is no way to say these are the same photon, much less say anything about a path from source to detector.

So, if you "shoot" singular photons, with an angle, through water, and you put detectors in the water, both straight ahead and where a light beam would go, you should determine if the refraction occurred. It was done?

 

[hutchphd]

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So, if you "shoot" singular photons, with an angle, through water, and you put detectors in the water, both straight ahead and where a light beam would go, you should determine if the refraction occurred. It was done?

How does this differ from taking an underwater photograph? Source is the sun, CCD in camera has many detectors (in an array). I have seen such photographs.
What does "shoot" singular photons mean???

 

[isotherm]

How does this differ from taking an underwater photograph? Source is the sun, CCD in camera has many detectors (in an array). I have seen such photographs.
What does "shoot" singular photons mean???

It is sending/emitting one photon at a time, like in the double-slit experiment.

 

[PeterDonis]

It is sending/emitting one photon at a time, like in the double-slit experiment.

Again, you have to be careful. In double slit experiments where the intensity of the source is turned down very low, the source is not emitting "one photon at a time". The state that the source emits is not a "one photon" state (Fock state); it is a coherent state. Thinking of it as one little billiard ball moving at the speed of light is not correct. Neither is thinking of it as "one photon's worth of a wave".

 

[isotherm]

Again, you have to be careful. In double slit experiments where the intensity of the source is turned down very low,...

Ok, but if was done? We used the same source (or similar) to determine refraction?

 

[PeroK]

Ok, but if was done? We used the same source (or similar) to determine refraction?

A percentage of light will reflect from water. That's an interesting question. If you emit one photon at a time, why do some photons pass through the water (and refract) and some reflect?

 

[Dale]

So, if you "shoot" singular photons, with an angle, through water, and you put detectors in the water, both straight ahead and where a light beam would go, you should determine if the refraction occurred. It was done?

What do you think is different in this question than in what I already posted? If the probability of a single photon refracts through a lens, what makes you think it wouldn’t refract in water?

 

[PeterDonis]

We used the same source (or similar) to determine refraction?

Yes.

 

[Vanadium 50]

If I search

So why should I bother writing an answer if you're just going to disregard what people write and ask a search engine or CrapGPT?

 

[PeterDonis]

If I search "speed of photon"

This is not a good way of understanding physics.

It is true?

It's too ill specified to even be evaluated as "true" or "false".

And "always" means also in a medium?

Even leaving aside what I said above, read what you quoted again. Does it say "in a medium"? No; it says "in" something else. What is that something else?

 

[renormalize]

Ok, but if was done? We used the same source (or similar) to determine refraction?

You can without a doubt measure the refraction of single photons. Here's one experiment by Wang and Strausser:
Single-photon determination of transmission, index of refraction and material thickness

 

[PeterDonis]

You can without a doubt measure the refraction of single photons.

"Single photons" here refers to the detectors used, which are discrete; they record individual "photon detections", not a continuous measurement of something like an electromagnetic field.

The states of the quantum EM field involved in these experiments, however, are, as far as I can tell, not Fock states; they are coherent states (from a laser via down conversion in a BBO crystal). These states are not eigenstates of photon number and cannot be accurately described as "single photon" states. They are the closest quantum analogue to classical "electromagnetic wave" states.

The extremely low intensity of the source in this experiment can also be taken to mean that the expectation value of photon number inside the experiment is no more than one; that is another sense in which the description "single photon" is sort of applicable. But the expectation value won't be exactly one, and doesn't correspond to any kind of "single photon" in the actual EM field state anyway.

 

[Dale]

The states of the quantum EM field involved in these experiments, however, are, as far as I can tell, not Fock states; they are coherent states (from a laser via down conversion in a BBO crystal)

Are there readily available sources that do produce Fock states?

 

[PeterDonis]

Are there readily available sources that do produce Fock states?

Not readily available, no. My understanding is that, while experiments have been done with such sources, they are hard to build and hard to do experiments with.

 

[vanhees71]

Again, you have to be careful. In double slit experiments where the intensity of the source is turned down very low, the source is not emitting "one photon at a time". The state that the source emits is not a "one photon" state (Fock state); it is a coherent state. Thinking of it as one little billiard ball moving at the speed of light is not correct. Neither is thinking of it as "one photon's worth of a wave".

You can nowadays do the double-slit experiment with single photons, and what you get is when repeating the experiment many times just the expected interference pattern.

It's of course wrong to think of photons as localized massless particles. They don't even have a position observable and thus photons cannot be localized in any classical-particle sense. As an intuitive picture it's usually best to think in terms of electromagnetic waves.

 

[Dale]

You can nowadays do the double-slit experiment with single photons,

What is the name of a source that produces a single photon Fock state? Or are you talking about coherent states with low enough amplitude that the expectation of more than one photon is negligible.

 

[isotherm]

You can without a doubt measure the refraction of single photons. Here's one experiment by Wang and Strausser:
Single-photon determination of transmission, index of refraction and material thickness

Very interesting. Thank you!

What do you think is different in this question than in what I already posted? If the probability of a single photon refracts through a lens, what makes you think it wouldn’t refract in water?

Sorry, somehow I missed your confirmation of refraction (post #4).

So, single photons do refract when entering in another medium. Does it mean that there is a decrease in speed (for single photons) when entering (from vacuum) in a medium with refractive index greater than 1? How/why is this (both the refraction and the possible decrease in speed) happening?

So why should I bother writing an answer if you're just going to disregard what people write and ask a search engine or CrapGPT?

The information was from google and wikipedia. And I really doubt that the quote (see post #6) was wrong. Was it? How it is correct?

 

[Nugatory]

You can nowadays do the double-slit experiment with single photons,

”Single-photon” in the sense that the detection events happen one at a time, or nthe sense that single-photon state has been prepared?

 

[isotherm]

The "waves" that explain interference in the double slit experiment for single photons are quantum waves, which are not the same thing as the "electromagnetic wave" that appears in Wikipedia's explanation.

So the interference in the double-slit experiment for "single-photons" is different, in result, from one recorded with a beam of light (with the same frequency)? If not, why not?

 

[vanhees71]

”Single-photon” in the sense that the detection events happen one at a time, or nthe sense that single-photon state has been prepared?

In the sense that you prepare a true single-photon state. That can be done by using parametric down-conversion, which creates entangled photon pairs by shining a laser on a birefringent crystal (like $\beta$-barium borate, BBO). Then you can use the one photon ("idler") to "herald" the presence of the other photon ("signal"), which you let go through the double slit. What you get is of course a random dot at the screen for each photon. The pattern that forms when you store all these dots after repeating the experiment with many equally prepared photons is the interference pattern you expect from the classical theory. The meaning is that the detection probability distribution is proportional to the (time-averaged) energy density of the em. field.

This is not too exciting, but you can of course do things with single photons very much different from classical em. waves, which from the point of view of QED are coherent states, even with very much dimmed-down ones (where you have mostly vacuum). One example is to make use of both of the entangled photons from parametric down-conversion to realize things like the quantum eraser (also in the Wheeler delayed-choice setup).

 

[PeroK]

So, single photons do refract when entering in another medium. Does it mean that there is a decrease in speed (for single photons) when entering (from vacuum) in a medium with refractive index greater than 1? How/why is this (both the refraction and the possible decrease in speed) happening?

There is no locally realistic picture of quantum mechanical phenomena, such as the refraction of light. If you set up an experiment with a light source and a detector, then you can calculate the probability of detecting a photon with the detector in any given position. In this case, the probabilities are consistent with refraction.

You really ought to read Feynman's notes on this:

https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

It's becoming a little tiresome that you are still pounding us with your locallly realistic questions on QM. Questions like "what was the photon doing while it was moving through the water?" and "what speed was it moving at time $t$?" are not questions that can even be asked in QM.

If you don't want to think quantum mechanically, then you should stick to classical EM and forget about photons - as they are elements of a QM theory of light and not the classical particles, that you been have repeatedly insisting on!

 

[vanhees71]

Indeed "the in-medium photon" is characterized by its in-medium spectral function, which can be calculated in many-body (relativstic) QFT. For a application of this in contemporary heavy-ion research, see, e.g.,

https://itp.uni-frankfurt.de/~hees/publ/habil.pdf

 

[Dale]

Does it mean that there is a decrease in speed (for single photons) when entering (from vacuum) in a medium with refractive index greater than 1?

Again, that question is fraught with all of the issues and caveats identified earlier. Insofar as, in my opinion, it can be answered at all, I already answered it. If you perform the experiment I indicated you will get the results described.

Again, make what you will of that. To me it is a “yes with lots of aforementioned caveats”.

I am not going to exclude the caveats, because they are important. But I also don’t want to simply surrender and say that the question has no part that can be answered. So I answer it by reference to an experiment.

 

[PeterDonis]

The information was from google and wikipedia.

And, as you were told in post #17, that is not a good way to understand physics, and what you quoted is not reliable information.

And I really doubt that the quote (see post #6) was wrong.

As you were told in post #17, it's too ill specified even to be evaluated as "right" or "wrong".

 

[PeterDonis]

So the interference in the double-slit experiment for "single-photons" is different, in result, from one recorded with a beam of light (with the same frequency)? If not, why not?

Apparently you aren't even reading what others are posting in response to you. The term "single photons" is not a good description of the experiments you are referring to. The only difference between what you are calling "single photons" and "a beam of light" is the intensity of the source: the quantum state emitted by the source is the same in both cases.

For a low intensity source (what you are calling, mistakenly, "single photons"), you can actually see individual dots on the detector screen. These detections are often referred to as "photon detections", but that does not mean what you think it means. It just means that the detections are discrete dots. It doesn't mean that the light in between the source and detector is "single photons". It's just a very low intensity coherent state--the same state as with a high intensity source (see below). Over time, the individual dots build up an interference pattern on the detector. This behavior is not explainable by classical waves; the Wikipedia article's explanation using classical waves does not explain why the detections are individual dots.

For a high intensity source (what you are calling a "beam of light"), it is no longer possible to see the individual dots; all you see is the interference pattern. The classical wave model used in the Wikipedia article can explain the interference pattern, but only if you ignore what the same experiment with a low intensity source is telling you about the individual photon detections. If you want to have a single model that explains both experiments, the classical wave model does not work. Only the quantum field theory model does.

 

[PeterDonis]

In the sense that you prepare a true single-photon state. That can be done by using parametric down-conversion

The input state to parametric down conversion is a coherent state from a laser. Does the BBO crystal somehow convert this into a pair of Fock states?

 

[isotherm]

Questions like "what was the photon doing while it was moving through the water?" and "what speed was it moving at time ?" are not questions that can even be asked in QM.

So, basically, we don't know what a photon "does" between emission and detection, but we also don't need to, because, using QM, we

can calculate the probability of detecting a photon with the detector in any given position

OK, I should probably buy Feynman's book. Thank you!I have one last question about photons in a medium: force carrier photons are always "traveling" with the speed c, regardless of the medium?

 

[PeterDonis]

So, basically, we don't know what a photon "does" between emission and detection

I have one last question about photons in a medium: force carrier photons are always "traveling" with the speed c, regardless of the medium?

You do realize that the first quote from you above, which is correct, means that the second quote from you above is a bogus question, right?