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Question about delayed choice quantum eraser

  1. Oct 9, 2008 #1
    I was reading about the Delayed Choice Quantum Eraser experiment here:

    bottomlayer.com/bottom/kim-scully/kim-scully-web.htm

    In this experiment the which-path info is erased or not at random AFTER the original (signal) photon hits the screen. The results of the screen are seen by the experimenter AFTER the choice to erase or not took place.

    I wonder what happens If the experimenter looks at the screen after the photons hit the screen but BEFORE the choice to erase the which-path is made? That is to have the idler photons still traveling and not reach yet the mirror that has a 50-50 chance of erasing the info.

    Any ideas?
     
  2. jcsd
  3. Oct 9, 2008 #2

    Hurkyl

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    If you're describing what I think you're describing....


    One of the main points (which, IMHO, is woefully underemphasized in popular accounts) is that the screen always looks 'normal'. The interference pattern only appears in post-processing, after you've separated the images on the screen into two sets based upon what the other detector saw. (And, of course, only appears if you retained the which-path info)
     
  4. Oct 10, 2008 #3

    Demystifier

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    Whenever I have conceptual doubts about delayed choice and quantum eraser questions, I use a trick: I first analyze what would be the answer in the Bohmian interpretation. Then I simply apply the theorem that states that measurable predictions of the Bohmian interpretation are identical to those of the standard interpretation. The advantage of this trick is that, even if you do not favor the Bohmian interpretation, this approach is conceptually simpler in the sense that it does not involve the wave-function collapse.

    To see in more detail how the Bohmian interpretation works for delayed choice, see:
    D. Bohm, C. Dewdney, B.J. Hiley, Nature 315 (1985) 294-297.
     
  5. Oct 10, 2008 #4

    vanesch

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    I do exactly the same thing with MWI :smile:
    It is my main - if not sole - justification for considering MWI.

    In fact, the reason why as well Bohm as MWI give clear answers in this kind of cases, is that they don't have a "measurement ambiguity" built in their formalism, but have a universal dynamics. In other words, you can "close your eyes and think of England" and let the formalism crunch the numbers - while in every projection-based viewpoint, you have to decide when you project and when you don't, and that's the difficulty here.
     
  6. Oct 10, 2008 #5
    Thanks guys for the response.

    Ok So let's see these 2 scenarios

    1) I look at the screen AFTER completely erasing the which-path info of all photons.
    I see the interference pattern. right?

    2) I look at the screen BEFORE completely erasing the which-path info of all photons. The idler photons have not reached the detectors yet.
    You say I see the the normal distribution. right?
    So in this case it doesn't make a difference if I see or erase the which-path info, I already saw the normal dist. and that won't change. right?
     
  7. Oct 10, 2008 #6

    atyy

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    Quantum Erasure: Quantum Interference Revisited
    Stephen P. Walborn, Marcelo O. Terra Cunha, Sebastião Pádua, Carlos H. Monken
    http://arxiv.org/abs/quant-ph/0503073

    "Wait Bob, that wasn’t there before! How did you make the photons interfere after I already detected them and recorded it all in my lab book?!”
     
  8. Oct 12, 2008 #7
    Thanks. I just read the article, very good by the way.

    So what I understand is that if you have any means to measure the which-path information (even if not measured yet), and you see the screen you will see the normal dist. If afterwards you erase the info from a subset of the photons, you can see interference only in that subset.

    But what about if you erase the info on all photons?
     
  9. Oct 12, 2008 #8
    Good article think I'll send it to a few non QM literate friends. Every time I read about Quantum Erasure I'm left with this odd niggling feeling that I'm peering through this strange lens called "entanglement" and that as I examine an object through the lens I can't decide if I'm changing my focus and thus seeing the a different aspect of the object or the object itself is changing.
     
  10. Oct 13, 2008 #9

    Cthugha

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    If you look at the paper you linked in your first post, you will notice, that there are two subsets - or joint detection rates - which can show interference if you destroy which-way information (Fig. 3 and 4). If you take a close look, you will notice that they are out of phase.

    If you erase which-way info on all photons and just look at the screen without choosing a subset by doing coincidence counting, you will now see both of these interference patterns superposed, which will again be a normal distribution as they are out of phase. So there is still no interference pattern without doing coincidence counting.
     
  11. Oct 13, 2008 #10
    Thanks for the response!

    Now this raises another question:

    In this experiment there is no interference without doing coincidence counting, but in the original double slit experiments the interference pattern is shown.

    So why is that, what is the difference between the two?
     
  12. Oct 14, 2008 #11

    Demystifier

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    An analogy from everyday life may also be helpfull:
    https://www.physicsforums.com/blog.php?b=7 [Broken]
     
    Last edited by a moderator: May 3, 2017
  13. Oct 14, 2008 #12

    Cthugha

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    Well the key to interference phenomena is indistinguishability of some sort. Comparing the simple double slit to quantum eraser experiments, you will notice, that we are talking about two different kinds of indistinguishability here.

    The usual double slit uses the fact, that there is a fixed phase relationship of the incident light at both slits. If the phases at both slits were completely independent of each other, this would be some kind of which way information and the interference pattern would disappear. In order to avoid this, you need light, which is at least a bit coherent: The coherence length needs to be at least as large as the slit separation is. The light, which comes out of a BBO crystal used for spontaneous parametric down converion is rather incoherent. However one can increase the coherence length by putting the BBO crystal far away from the double slit. This equals choosing a small subset of wave vectors (or equivalently emission angles), which actually make it to the double slit, so the phase relationship at the double slit is better defined.

    Quantum erasers and the like use indistinguishability of two-photon amplitudes. In this case the phase relationship of the two-photon state is well defined as the wave vectors of the two photons are correlated due to conservation of momentum. The detector D0 is positioned in the focal plane, so that each point inside the focal plane corresponds to exactly one wave vector. If the detector is small enough, this is a rather precise measurement of the photon wave vector.

    Now the other entangled photon hits a double slit or some other kind of similar setup like in the paper you quoted. The light hitting this double slit is alone not coherent enough to show an interference pattern as there are plenty of different wave vectors arriving. However, if we detect a photon at the other detector, we measured the wave vector and therefore the wavevector of the other photon is pretty well defined due to conservation of momentum. So the subset of these joint detections has a clearly defined wave vector and therefore there will be some kind of interference effect in the coincidence counts.

    However, to actually see an interference pattern in the coincidence counts at D0, you need a rather large spread of wave vectors, as every position in the plane corresponds to one certain wave vector. So the more wave vectors you include, the better will the visibility of your interference pattern be.

    Now one sees that finding interference in the usual double slit needs a small spread in the wave vectors (which can be achieved by using a huge distance between light source and double slit) and finding interference effects in coincidence counting experiments needs a large spread in the wave vectors (which can be achieved by using a small distance between light source and double slit). As you can't have a small and a large distance simultaneously, both kinds of interference are complementary, so you can't have both at the same time with full visibility.
     
  14. Dec 2, 2008 #13
    Sorry in advance if this is an observation already covered but. In reference to the Delayed choice quantum eraser experiment http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser What would happen if BSa/BSb were moved so that the time taken for the idler photon to reach BSa/BSb was greater than the time taken for the signal photon to reach D0? i.e. the "choice" is made after the detection of the signal photon. (I'm also making the assumption that the data from D0 is not viewed until after the data from D1/D2/D3/D4)
     
  15. Dec 2, 2008 #14

    Cthugha

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    Although Wikipedia is usually not a really reliable source, your question is already answered in the article you quote. It does not matter, whether the path to D0 is shorter or longer than the other path. You will get the same results in both geometries. Additionally it does not even matter, whether you have a look at the data from D0 before the idler photon arrived at the other detector. You never get any information from looking at D0 alone.
     
  16. Dec 2, 2008 #15
    If I've understood the experiment correctly, the idler photon is detected 8ns after the signal photon. However, there is no mention of the time at which the idler photon passes through BSa/BSb(the aparatus that give the idler a 50/50 which path/hidden path status). I have made the assumption that the transition through BSa/BSb is before the signal photon is detected. I may be wrong but I believe there is an important distinction between the idler passing through BSa/BSb before the signal detection and passing through after the signal detection. That is to say, if the idler photon passes through BSa/BSb after the signal photon is detected and D0 shows an interference pattern or a cluster pattern in keeping with the "which path" or "hidden path" results, then wouldn't this indicate something very strange happening? Again, apologies if I'm missing something obvious.
     
  17. Dec 2, 2008 #16

    Cthugha

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    Well I don't know, how well you know the experiment, so let me start by asking you a question about the most important aspect:

    Is it clear to you, that you will NEVER see an interference pattern on D0?
     
  18. Dec 2, 2008 #17
    If the signal photons that are paired with the idler photons that got diverted to the hidden path detector are plotted will they not show interference?
     
  19. Dec 2, 2008 #18

    JesseM

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    As the wikipedia article explains, the total pattern of signal photons never shows interference, it's only when you look at the subset of signal photons whose matching idlers were detected at a particular detector (one of the 'which-path erasing' detectors) that you find an interference pattern. Re-read these parts of the article:
    and
     
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  20. Dec 3, 2008 #19
    "If the signal photons that are paired with the idler photons that got diverted to the hidden path detector are plotted will they not show interference?"

    My conjecture with this question was that they(the D0/D1 and D0/D2 subsets plotted separately)would(was I right?). I was just curious as to what would happen if the experiment was repeated with a minor adjustment. The aparatus dealing with the idler photon being repositioned so that there would be a greater time for the idler photon to reach the beam splitters BSa/BSb than for the signal photon to reach D0.
    As the experiment stands(sorry if I'm wrong about this and thankyou for your patience) there is a 8ns delay between the registry of the signal photon and its entangled idler(the idler being detected 8ns after the signal). However, for me, the crucial piece of the aparatus are the beam splitters BSa/BSb as it is here that the "fate" of the idler and its entangled signal photon are decided. So the fact that the idler photon is detected at D1/D2/D3/D4 8ns after the detection of the signal photon at D0 is irrelevant because BSa/BSb are encountered before the signal photon is detected at D0(this is an assumption on my part because I can't find any measurements on this). So, if this experiment was repeated in such a way that the signal photon was detected at D0 before the idler photon encountered BSa/BSb and the data was retrieved and plotted in the exact same way as before(data from D1/D2/D3/D4 was viewed then the data from D0 and the subsets were plotted) would an interference pattern in the D0,D1 and D0,D2 subsets still be seen?
     
    Last edited: Dec 3, 2008
  21. Dec 3, 2008 #20

    JesseM

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    Yes, the D0/D1 and D0/D2 subsets individually show interference--I wasn't sure if you understood that the total pattern of photons at D0 does not show interference.
    I can't be certain that this is true of the experiments that have been done, but I'd imagine it would be--the diagrams of the setup show the detectors being close to the beam splitters, most of the longer path length for the idlers being prior to the point they reach the splitters. Anyway, I'm pretty sure the prediction of quantum theory would be that whether the signal photons reach D0 before or after the idlers reach the beam splitters shouldn't affect the outcome--either way you'd still see no interference in the total pattern of photons at D0, but if you plotted the subset of signal photons whose idlers when to D1 or D2, you'd see an interference pattern in this subset. Perhaps someone else can verify this?
     
  22. Dec 3, 2008 #21

    Cthugha

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    Maybe one should add, that the Gaussian peak at D0 alone is in fact the superposition of both (D0/D1 and D0/D2) interference patterns. They are phase shifted by pi (as can be seen in the Kim paper) and therefore superpose to a simple peak.

    There have been experiments showing this. I will have a look. Maybe I can find them.

    The beam splitters are not that crucial as you might think. There is no measurement done by splitting the beams. For example you could recombine the beams in a Mach-Zehnder-interferometer like way and thereby destroy the which-way info again. The important point is the measurement.
     
  23. Dec 3, 2008 #22
    Although there is no measurement done at the BS, it is here that the ultimate arrival point of the idler is determined(D1/D2 or D3/D4). If you were to introduce a new piece of aparatus after the BS wouldn't you be merely moving the point of determination?(either forward or backward depending on what the new aparatus does).
    I'll try to illustrate my point about the importance(just guess work really) of the position of the BS.

    signal}----------------D0
    idler }--------BS--------D1/D2 or D3/D4
    In this scenario, the signal photon is "aware" of the destination of the idler photon before it(the signal photon) appears at D0. The possible detection points of the idler photon before arriving at BS are D1/D2 or D3/D4. That is to say, after passing BS the destination point of the idler has been decided at either a which-path detector(D3/D4) or a path-hidden detector(D1/D2) and so the signal photon can appear at D0 accordingly.

    signal}----------------D0
    idler }-------------------BS--------D1/D2 or D3/D4
    In this scenario, the signal photon cannot be "aware" of the destination of the idler photon as it has yet to pass the BS. So I guess my questions are:
    1) Do the D0/D1 and D0/D2 subsets in the second scenario still display interference?
    2) HOW?

    I'm using the word "aware" to replace intanglement phenomena which I am unfamiliar with. I'm also perposely ignoring the retro-active input of an observer(if it's relevant). Please pick me up on either of these.
     
  24. Dec 4, 2008 #23

    Cthugha

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    Not necessarily. The important point is, that there is the possibility to be unable to determine which-way information. For example:

    signal}------------D0
    idler}------BS-----------\
    | |
    | |
    \------------BS----D1
    |
    |
    D2

    In this setup, you split the beam, but destroy the which-way information again. In this kind of setup there will be interference in D0/D1 and D0/D2 as long as you do not add another measurement, which determines, which way a photon took.

    1) Yes!
    2) Well remember, that this is two-photon-interference. In usual interference, you have a superposition of two probability amplitudes, which lead to the same outcome, but cannot be distinguished experimentally. The key property here is coherence as only a fixed phase relationship over time spans, which are longer than the difference in travel time of the two alternative paths, assures that there is no possibility to determine which way information.

    In two-photon-interference, the situation is more or less the same, but the coherence properties are different. Both beams are pretty incoherent for themselves. That is a reason, why there is no interference pattern looking just at D0. Single beam coherence is lost pretty fast, but - due to the entanglement - the two photon state is pretty coherent. So in this case you have also the interference of two probability amplitudes - the two paths the photon can take to D1 or D2, but only the coherence time of the two-photon state is long enough to show this effect.
    The key is really, that you will not get right results, if you think of seperate photons. As soon as you think of two-photon states, the situation gets much easier to handle.
     
  25. Dec 4, 2008 #24
    signal}------------D0
    idler}------BS-----------\
    | |
    | |
    \------------BS----D1
    |
    |
    D2

    sorry but I can't understand this schematic.

    So would it be true to say that both the signal and idler probability waves run through both sides of the aparatus?(the signal path and the idler path), is this what you mean by entanglement coherence? And that from the photons point of view it appears at the signal and idler destination at the same time? So from an observers point of view the coincidence counter would(in this case) show a 8ns delay between D0 and D1/D2/D3/D4, whereas from the photons point of view, no such delay ever existed?
     
  26. Dec 5, 2008 #25
    Can I ask what is essentially my main question about the delayed choice theory in a much more simplistic way?

    If the decision to view or erase the which-way data is made after the photon, from the observers point of view, has arrived at the end location. Will the results be the same as if we were viewing(or not viewing) the which-way data live? That is to say, will an interference pattern be observed in the subsets that have had their which-path data erased without being viewed? I'm not asking how or why at this point.

    I'm really sorry if this question crops up often and has been dealt with before. So again, to all, thanks for your patience.
     
    Last edited: Dec 5, 2008
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