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I Interference of a single photon in an interferometer

  1. Jul 13, 2017 #1
    I think we can all agree that when we are shooting many photons one by one, through an interferometer, we can eventually land up with the interference pattern. This can be explained by saying that two photons combining in some areas to give four photons and in some places annihilating each other. This violates the conservation of energy so a more plausible reasoning would be to assume that every photon interferes with itself only to preserve local conservation of energy.

    However, I have a problem with this for in the interferometer set up where we are splitting one beam into two parts, we still get an interference pattern with arms of different lengths. This would mean that no single photon that gets "split" into two states of motion ( two beams travelling in different arms ), arrives at the same time, at the screen or sensor. So how is it even possible to get the interference pattern? ( which we do get experimentally )

    In his book, principles of quantum mechanics by Dirac, he mentions that when the beam is split in two different components we should still regard them as being one entity with a superposition of two wavefunctions (for two beams); But doesn't the very act of splitting disturb the photon and cause it to already collapse or make it's mind to go in one of the arms? Is it just that we're unaware of the direction the photon choose and so we use superposition to address our uncertainty of the situation?

    In case of the double slit experiment I think a similar situation arises since the most points on the screen are at different path lengths from the slits from which wavefunction gets split.

    TLDR:

    How do we explain single photon interference in an unequal arm length interferometer? Do we simply accept that it is a fact of nature that when we do the experiment with a large no. of photons we get the familiar interference pattern because single photon interference has no meaning?
     
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  3. Jul 13, 2017 #2

    zonde

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    The idea that photon interferes with itself is experimentally falsified by this experiment:
    Interference of Independent Photon Beams
    [Mentor's note: This post has been edited to prevent this thread from being hijacked and turned into an interpretational debate. We don't need to go there quite yet, as this thread is about accuratelly and completely describing the many strange and counterintuituve things that happen in multi-photon systems]
     
    Last edited by a moderator: Jul 13, 2017
  4. Jul 13, 2017 #3
    Doesn't that violate local conservation of energy? The very thing that led to the idea of the photon interfering with itself in the first place?
     
  5. Jul 13, 2017 #4

    zonde

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    I'm not sure what do you mean. How experiment can violate conservation of energy? It is model that can do that.
    Maybe you mean that this experiment can't be explained by any model that conserves energy?
     
  6. Jul 13, 2017 #5
    The theory that the photon is interfering with itself does not violate conservation of energy. The theory is not that two photons exist at one time, but that there is a superposition of the photon. In the two slit experiment, the whole notion that the photon follows a trajectory is discounted. The photon is emitted and is then detected at the screen.

    Once detected, there is no evidence remaining that would indicate which slit it had traveled through, and thus it should not be viewed as having transited either slit. It should certainly not be viewed as there being two photons, one each for each slit.

    A better example is the interferometer experiment where "nulls" in the interference pattern can be eliminated by blocking one of the two interferometer paths. The photons that land in those nulls do so because they could have hit the block, but didn't. That should clearly demonstrate that there is only one photon and that it's final detected position is not the result of a simple trajectory.
     
  7. Jul 13, 2017 #6

    Nugatory

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    It does not - Pfleegor and Mandel's work, cited by Zonde above, is sound. It also doesn't falsify the statement that a photon interferes with itself; it falsifies the statement "a photon only interferes with itself". Googling for "Pfleegor Mandel interference" will bring up many of these subtleties.
     
  8. Jul 13, 2017 #7
    In 'Quantum Mechanics, 3rd Ed by S. Gasiorowicz, the author discusses the relevant portion of Dirac's text in the very beginning of Chapter 2 to motivate the validity of Schrodinger's equation. I will quote the relevant text here as it can shed some light sn the matter at hand:

    Supplement 18 A can be accessed in the link below and provides a quantum field theoretic treatment of the photon.
    http://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=1533&itemId=0471057002&resourceId=1342
     
    Last edited: Jul 13, 2017
  9. Jul 13, 2017 #8
    Just noting that we have yet to address the the OP's 1st question:
     
  10. Jul 14, 2017 #9

    zonde

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    If the photon self interference is the only way how to explain double slit interference then we are left with no explanation for Pfleegor Mandel interference experiment.
     
  11. Jul 14, 2017 #10

    zonde

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    Well, if we could explain Pfleegor Mandel interference experiment then the same explanation should work for unequal arm length interferometer.
    So I think that discussion is closely related to OP question.
     
  12. Jul 14, 2017 #11
    I recommend to read: "Interactive tutorial to improve student understanding of single photon experiments involving a Mach–Zehnder interferometer" by Emily Marshman and Chandralekha Singh (Eur. J. Phys. 37 (2016) 024001 (22pp)) (http://iopscience.iop.org/article/10.1088/0143-0807/37/2/024001)
     
  13. Jul 14, 2017 #12

    vanhees71

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    The explanation of the experiment is given in terms of standard QED in the above cited paper. As to be expected QED works.

    Strictly speaking the experiment tests the interference effect not between two independent single photons but between two low-intensity coherent states. Nowadays the experiment should also be doable with true single-photon sources. I do not know, whether this has been done yet.
     
  14. Jul 14, 2017 #13

    Unless there is a measurement device on either arm of the experiment, we cannot say that the photon has either been transmitted or reflected, we thus have an "entity" which can formally be "described" as a superposition of two wavefunctions. A quantum mechanical superposition has nothing to do with the classical understanding that something is - with some probability - either there or there. The quantum mechanical “ ǀphoton in arm#1> AND ǀphoton in arm#2> “is fundamentally different from the classical “ ǀphoton in arm#1> OR ǀphoton in arm#2> “. There is no way to bridge this abyss. Take it as it is.
     
  15. Jul 15, 2017 #14
    That is not what I meant by violation of conservation of energy. It was in the Dirac's book where I read that the motivation for considering photons interfering with themselves comes from the fact that we cannot have two photons meet up at a screen to produce 0 photons or 4 photons at the minima and maxima respectively, as would be explained by a classical physicist. The trouble I have is addressing the question that If I have a system where I can split a beam of light into two components with different transit times to the screen and obtain the same interference pattern, how would this make sense when I am shooting photons one by one. One of the split component always reaches the screen after its partner has arrived.
     
  16. Jul 15, 2017 #15
    Consider the double slit experiment for a single photon source, if we are to just imagine the probability wave goes through both slits then the distance to a point at the screen will be at unequal intervals too from the two slits. Then the probability wave arising from slit 1 and from slit 2 must interfere because that is what we do in quantum mechanics. We take state 1, take state 2, add them, square them and say that's the probability of finding the photon there. But notice how if we are to assume state 1 and state 2 follows the same time evolution laws i.e. the same speed of propagation then they never make it to the same place on the screen on time.
     
  17. Jul 15, 2017 #16
    I know it is not wise to consider the probability waves as something analogous to a real wave propagating through space but most quantum mechanics books address the double slit experiment through this way. As for the QED explanation I'm not there yet to fully understand it.
     
  18. Jul 15, 2017 #17

    vanhees71

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    I never understood what's meant by the phrase "a photon (or a massive particle) interferes with itself". Usually what people mean is a single-photon/particle state which they write as the superposition of other single-photon states. There's nothing mysterious about this.
     
  19. Jul 15, 2017 #18
    The confusion I think comes from introducing the idea of photon self-interference in the first place.
     
  20. Jul 15, 2017 #19

    Nugatory

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    You are making the assumption that there's a single moment of emission so that both paths are starting at the same precisely defined point in space and time; this is basically classical thinking sneaking back in. If you don't make this assumption there's room for overlap at the detector even when the path lengths are different.
     
  21. Jul 15, 2017 #20
    But the emission started out as a one photon given by one state vector at the laser source.
     
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