Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Can one photon interfere with another photon?

  1. Jul 14, 2014 #1
    Hi Everyone

    This may sound like a question with an obvious answer but with my current knowledge, it is not obvious to me. Can one photon interfere with another photon or can each photon only interfere with itself?

    Most people on this forum will know that Young's Slits produces interference patterns even with "one-at-a-time" photons. This means that it is not necessary for one photon to interfere with another photon in order for Young's Slits to produce an interference pattern.

    One way of looking at this question is as follows: Imagine that you have two seemingly identical beams of parallel light which are as powerful as each other and have exactly the same pure wavelength. Let's say the two beams are coming from two unmarked emitters so that you can't tell exactly how each emitter is producing its beam but you have been told that one of the emitters is a laser device which produces completely phase-aligned light and the other emitter contains just a normal but powerful LED which produces light which is not phase-aligned. Can Young's Slits tell the difference between the two beams? Can the normal but powerful LED produce visible interference patterns?

    If it is not possible to tell the difference between the two beams using Young's Slits then I would say that this would mean that one photon cannot interfere with another photon. What do the experts on this forum think?

    Thank you very much.
     
  2. jcsd
  3. Jul 14, 2014 #2

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    No.

    Its obvious why not when you see a correct analysis of the double slit experiment:
    http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

    But I also have to say since all photons are equivalent the question is in some sense ambiguous.

    Thanks
    Bill
     
    Last edited: Jul 14, 2014
  4. Jul 14, 2014 #3

    DrChinese

    User Avatar
    Science Advisor
    Gold Member

    I have always seen this particular question as a bit complex (and having nothing to do with a double slit setup). Some assert that independent photons cannot interfere, and others call it the other way. Here is one article:

    http://arxiv.org/abs/1112.1943
    Quantum interference between two single photons of different microwave frequencies
     
  5. Jul 14, 2014 #4
    Hi Bill

    Thank you very much for your reply. I would be very grateful if you could clarify your answer by answering the following two questions:

    1. Does a beam of light have to be phase-aligned in order to produce visible interference patterns?

    2. Can two independent laser beams produce visible interference patterns when shone onto the same spot?

    If I am interpreting your answer correctly, then I think your answer to both of the above two questions ought to be "no".

    Thank you very much.
     
  6. Jul 14, 2014 #5

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    One thing that I am uncertain about when it comes to interference is understanding the relationship between quantum interference and classical interference. The electromagnetic field, being a tensor-valued field, exhibits interference classically: You add up the fields due to two (or more) sources to get a resulting field. The intensity for the resulting field will in some places be less than either field separately (destructive interference) and will in some places be greater than either field separately (constructive interference). This classical notion of interference, I would think, still applies quantum-mechanically. An E&M wave could be understood as the effect of many, many photons, and it seems to me that it would interfere with a second E&M wave consisting of many other photons.
     
  7. Jul 14, 2014 #6
    Thank you DrChinese and Stevendaryl for your replies.

    I am getting the impression that there does not seem to be a clear answer to my question. I wish I had access to an appropriately equipped lab so that I could attempt to find out the answer myself. How difficult would it be to build a device which uses a powerful pure-wavelength LED to produce a non-phase-aligned beam which looks exactly like a laser beam?
     
  8. Jul 14, 2014 #7

    Cthugha

    User Avatar
    Science Advisor

    Young's double slit experiment is fully classical and works on the field level. In fact it is a measurement of spatial coherence, which is more or less the angular size of the light source as seen from the double slits. As a consequence you can take any light source in the world and will get exactly the same interference pattern if you

    a) filter it spectrally such that you get the same spectral distribution
    b) filter it in real space using a pinhole such that you get a point-like light source
    c) adjust it to the same brightness

    So the double slit cannot distinguish between different light sources. However, there are other kinds of measurements which can do that. The double slit just measures first order coherence (see http://en.wikipedia.org/wiki/Degree_of_coherence).

    If you go to higher oder coherence, you will indeed find that multi-photon interference is possible. However, one needs conditional measurements to test that. Usually you split your light field, put it on two photodiodes and measure the conditional probability to detect a photon at a delay tau at detector 2, if you already detected a photon at time 0 at detector 1. The simplest and best known two-photon interference effect is the so-called Hong-Ou-Mandel dip (http://en.wikipedia.org/wiki/Hong–Ou–Mandel_effect) which is a standard experiment to check whether two single photons are indistinguishable or not.

    However, one should keep in mind that this kind of interference is very different from what one typically has in mind when thinking about double slit experiments.
     
  9. Jul 14, 2014 #8

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Of course not. You can do it with ordinary light that is anything but.

    No - the thing I am pretty sure is if they are correlated - independent laser beams are by definition not correlated.

    Thanks
    Bill
     
    Last edited: Jul 14, 2014
  10. Jul 14, 2014 #9

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Like I said since photons are indistinguishable the question is a bit ambiguous - the out being if they are entangled in some way.

    I do not think uncorrelated photons can interfere.

    Thanks
    Bill
     
  11. Jul 14, 2014 #10
    Firstly, thank you Bill for your latest replies.

    Thank you Cthugha for your reply. To be honest, the end of your penultimate paragraph went a bit beyond my knowledge of physics and I think that the Wikipedia article for the Hong-Ou-Mandel effect does not give a very good explanation for a layman. However the gist I get is that under certain circumstances, two separate photons can "extinguish each other" as Wikipedia puts it when they meet at a beam splitter. If this is correct, where does the energy go?

    Edit: Am I correct that photon extinguishment would happen when one photon is reflected and the other passes right through?

    Edit: Can you give a layman's explanation for the different orders of coherence?

    Thank you very much.
     
    Last edited: Jul 14, 2014
  12. Jul 14, 2014 #11

    Cthugha

    User Avatar
    Science Advisor

    Right. It is not written too well. Let me sum it up.

    You have a beam splitter with two input ports (I1 and I2), two output ports (O1 and O2) and two indistinguishable photons (P1 and P2) arrive at two different entry ports. Now there are 4 possibilities:

    a) P1 gets reflected, P2 gets transmitted: Both photons leave via O2.
    b) P1 gets transmitted, P2 gets reflected: Both photons leave via O1.
    c) Both photons get transmitted: One photon leaves via O1, one photon leaves via O2.
    d) Both photons get reflected: One photon leaves via O1, one photon leaves via O2.

    c) and d) lead to the same final situation. So if the photons are indistinguishable, you need to add the probability amplitudes for these two paths and square afterwards to get the probability for this event. If the photons are distinguishable, you just take the square for each single path and just add the probabilities. Due to the phase shift occurring upon reflection at a beam splitter, the probability amplitudes for c) and d) will always interfere destructively and this event will not take place.

    So, the photons do not extinguish each other, but they will form a bunch of two photons leaving via the same exit port. It will never happen that you find one photon emerging from each output port. This is an interference process involving two photons. However, it is usually considered as misleading terminology to consider this as the interference OF two photons. One should rather consider it as an interference of probability amplitudes for events containing more than one photon.

    A classic paper discussing that issue is "Can Two-Photon Interference be Considered the Interference of Two Photons?" (Phys. Rev. Lett. 77, 1917 (1996)). Also available from NIST, if you do not have a subscription for PRL: http://physics.nist.gov/Divisions/Div844/publications/migdall/psm96_twophoton_interference.pdf
     
  13. Jul 15, 2014 #12
    Compare a pair of radio antennae.
    They certainly can operate completely independently.
    Yet you can easily make them operate at pretty exactly same frequency, and at a specific phase relationship.
    So radio wave photons from two independent but synchronized antennae can certainly give interference pattern.
     
  14. Jul 15, 2014 #13
    Hi Cthugha and Bill

    Firstly, Cthugha, thank you very much for your latest reply. I think it is somewhat clearer than the Wikipedia article.

    Bill, I just want to clear something up here. What precisely do you mean by "equivalent" and "indistinguishable"? Do you mean just simply identical or do you mean something more than this? I may be wrong but it sounds slightly as if you think that there is actually no such thing as a completely individual, discrete photon. Am I correct?

    Do you think that on some level (a level which does not effect Young's Slits but which possibly does effect the Hong-Ou-Mandel effect), all photons in the Universe of exactly the same wavelength share the same vast communal wavefunction?

    Thank you very much.

    Cthugha, I Have five questions I would like to ask about this:

    1. In a typical Hong-Ou-Mandel experimental setup, are two separate emitters used to generate the two photons entering on either side of the beam splitter?

    2. In order to "interfere" with each other, do the two photons have to enter the beam splitter at exactly the same place on either side of the beam splitter? If yes, how is this precision achieved?

    3. If one of the beams is already phase-shifted by half a wavelength before entering the beam splitter, does this mean that instead of possibilities c) and d) not taking place, possibilities a) and b) don't take place instead?

    4. When the two photons leave the beam splitter, are they side-by-side or is one behind the other or are they positioned relative to each other in some other way? How do we know that two photons are leaving the beam splitter?

    5. Do you think it is possible that the true explanation of the Hong-Ou-Mandel effect may actually have nothing to do with the square root of probabilities? I am thinking that it might be the case that a more classical mechanism is operating whereby the beam splitter contains a vast number of tiny molecules which behave as randomly directed "one-way valves" (like in plumbing) which only allow photons to travel in one direction. It may be that these molecules act differently on photons of different wavelengths. Do you think that I might be on to something here?

    Thank you very much.
     
  15. Jul 15, 2014 #14

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    As I said in a previous post, you can certainly have classical interference between electromagnetic waves. If you have two sources of E&M waves, they will constructively or destructively interfere at a point depending on the difference of the two phases. What does that mean for photon interference? I'm not sure. I don't know what the description of a propagating macroscopic electromagnetic field would be in terms of photons.
     
  16. Jul 15, 2014 #15
    Thank you, Stevendaryl for your post. I may be wrong here but I think that the square of the field strength at each point in a "propagating macroscopic electromagnetic field" corresponding to an individual photon is proportional to the probability value of the same point in the photon's probability distribution.
     
  17. Jul 15, 2014 #16

    Cthugha

    User Avatar
    Science Advisor

    One could do that, but the easiest way is to take consecutive single photons emitted from the same source and a delay line.

    You need reasonable overlap of the modes. In reality each lab will have their own technique to achieve that. One way lies in coupling the single photons into fibers. This way you can first couple a bright laser into the fibers, adjust the optics such that the overlap at the fiber output is ideal and then you can remove the laser an start coupling the weak single photon signal into the fibers.

    No. The phase shift occurs in the two-photon probability amplitude between transmission/transmission and reflection/reflection and does not really depend on the initial phase (which is ill defined for single photons anyway). The Mandel/Wolf has a good description of this topic.

    You get a n=2 Fock state containing two absolutely indistinguishable photons.

    No. You are absolutely not on to something. You will get both photons leaving via exit port 1 50% of the time and both photons leaving via the other exit port 50% of the time. This does not depend on the wavelength, the material used for the beam splitter or even the beam splitter design as long as the beam splitter is 50/50. This has been verfied experimentally thousands of times in very different settings and for very different sources. Please do not make the mistake of guessing and formulating personal theories before actually learning in detail about a topic.
     
  18. Jul 15, 2014 #17
    Hi Cthugha

    Thank you very much for your reply.

    Am I correct in thinking that the delay line would be applied to one of the two paths to ensure that two probability sub-distributions of the same photon cannot arrive at the beam splitter at the same time?

    I am not entirely sure of what exactly you mean by the "modes". Do you mean the areas on the beam splitter where the probability distributions of the photons will land? Am I correct that by using fibers or some other method, these areas will be made as small as possible?

    By-the-way, was my reply to Stevendaryl correct? (Post #15)

    Thank you very much.
     
  19. Jul 15, 2014 #18
    If photons cannot interfere with photons, then what in the world are they interfering with in a double slit experiment? There is nothing supposed to be there but the slit and the photons, and if it is not the photons, it must be the slit. Would edge-diffraction not produce the same pattern even without any interference?


    They start talking about interference and end up talking about entanglement. What does quantum entanglement have anything to do with wave interference?
     
  20. Jul 15, 2014 #19

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Themselves? Nothing? You choose. It's best not to look at photons as sometimes a particle, sometimes a wave. They are quantum mechanical objects. Trying to make a classical analogy just doesn't work sometimes.

    Suppose you perform the double slit experiment with the incoming light reduced to such an extent that only one photon at a time passes through the slits. You'll still see an interference pattern arise over time as you accumulate where those individual photons are observed to hit the detector. With what do those single photons interfere? Certainly not other photons; there are no other photons in these single photon / double slit experiments. Yet the interference pattern still arises.
     
  21. Jul 15, 2014 #20

    DrChinese

    User Avatar
    Science Advisor
    Gold Member

    In any double slit setup, it is SELF interference. That is not usually obvious because there are so many photons present. It is much more obvious when something with a rest mass is diffracted through the slits. Self interference is the quantum effect being observed. Please note that interference is also a classical wave property, which makes it somewhat confusing to distinguish one from the other.

    Edge diffraction has nothing to do with an interference pattern either way, that only determines the shape of the bars. The only thing that determines the interference pattern is whether which-slit information is potentially available.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Can one photon interfere with another photon?
  1. Photon interference (Replies: 3)

Loading...