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Variation on Dopfer Experiment - Why Won't This Work?

  1. Apr 4, 2008 #1
    FTL Signaling with Dopfer - Why Won't This Work?

    I think at the outset we will all agree that the following will not work, but the more interesting question will be why.

    Take the Dopfer experiment described at:

    On page 36, Dopfer shows an apparatus consisting of an "upper half" and a "lower half", each corresponding to one of two entangled photons. The "upper photon" is sent to a Heisenberg lens which focuses parallel photons to a single point on the focal plane. The detector D1 is placed fixed at the focal point. Photons in the "lower half" are sent through a double slit and then to a detector D2 which scans the x-axis. An interference pattern emerges when the photons are correlated with those in the upper half that have been detected at the focal point. The detection at the focal point results in position information being utterly destroyed, thereby allowing the interference pattern in the lower half to emerge.

    JesseM and I have discussed extnesively why the coincidence circuitry is necessary and the conclusion we both reached is that with each position of D1, only a subset of photons is detected with position information destroyed; for the rest, it is possible, at least in principle, to detect position information. The only way to correlated that subset in the upper half with image-generating photons in the lower half is with slower-than-light coincidence circuitry.

    And so I asked, what would happen if we destroyed position information for ALL the upper half photons corresponding to lower half photons that went through the slits? Would ALL of the lower-half photons going through the slits therefore generate an interference pattern? If so, could this not be used as the coveted switch to send a binary FTL signal?

    So the means I thought of to destroy the position information in the upper half photons is as follows. In points in space in the upper half corresponding to the slits in the lower half, place two small biconvex lenses such that the focal point of those lenses is placed exactly where the slits would be in the lower half. All photons passing through those focal points will emerge parallel from the lenses. Then when those photons reach the Heisenberg lens shown on page 36 of Dopfer's thesis, ALL of them will strike the detector D1, thereby destroying position informaiton.

    The question is: will an interference pattern then emerge from ALL photons striking detector D2, eliminating the need for coincidence counting? If not, why not?

    Jesse suggested that placing the small converging lenses in the upper half might be problematic due to the HUP, that by isolating the photons to two small points in space, there is too much uncertainty in their momentum to ensure that they reach the correct lens and emerge parallel. However, the radius of the lenses could be large enough to account for the uncertainty, since the focal points would be quite small (5 mm or so).

    So, why won't this work?
    Last edited: Apr 4, 2008
  2. jcsd
  3. Apr 4, 2008 #2
    For those that might object that we can't control which directions the entangled photons will travel out of the crystal, and therefore we can't actually ensure that all of the photons that reach the slits have had their twins' position information destroyed, Cramer's experiment actually addresses this:

    "An argon-ion laser producing vertically polarized 351 nm UV light pumps a beta barium borate (BBO) crystal, producing two 702 nm infrared photons that are collinear with and momentum-entangled with the pump beam by the process of Type II collinear spontaneous downconversion."

    He then uses a polarizing splitter to separate the two entangled photons, and therefore can ensure that each member of the pair is directed to the appropriate apparatus.
  4. Apr 5, 2008 #3
    Wow. More than a day and no one has any thoughts? :)

    Another point I'd ask about is what can we say about the photons once they've been collimated by means of the two small lenses? Do they now have very precise momentum and therefore imprecise position? Can we no longer be sure they'll all strike the heisenberg lens?

    On the flip side, couldn't we make the heisenberg lens arbitrarily large to compensate for this?
  5. Apr 7, 2008 #4


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    peter, since we had a little PM exchange on this, would you mind if I just quoted our PMs and then offered my response to your last PM here?
  6. Apr 7, 2008 #5
    Oh, of course. :)
  7. Apr 7, 2008 #6


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    OK, here was our PM discussion (anyone interested in following this discussion should consider taking a look at my discussion with peter starting in post #40 of this thread):
    In response to your last comments, I had two thoughts:

    1. Normally when you see a calculation of how much uncertainty is added to the photon's momentum when it goes through the slits, it's assumed that the photon's wavefunction impinging on the slits was a plane wave with a perfectly well-defined momentum, and total uncertainty about position. In contrast, in this experiment the photons came from a known initial position, so there must already have been a certain amount of uncertainty in their momentum before going through the slits. Perhaps this point isn't too important though--ideally it might be possible to make the initial uncertainty in momentum arbitrarily small by making the source sufficiently far away.

    2. Your argument is based on running the Heisenberg microscope backwards, so that photons emerging from a single point in the focal plane of each of the two small lenses are perfectly collimated by the lenses. But this only works perfectly if all the photons going to one of these lens came from precisely one point in the focal plane--if the slits have some finite width, then the photons coming out of the lenses won't be perfectly collimated. You can make the slits smaller, but this makes the uncertainty in momentum of the photons coming out the slits greater, which takes us back to the problem I mentioned that some photons might go to the "wrong" lens or miss the lenses altogether. Perhaps if we actually did the detailed math here, there would be some tradeoff between photons that aren't detected because they aren't perfectly collimated by the two small lens and thus aren't focused to the position of the detector behind the third larger lens, and photons that aren't detected because they didn't actually go to the small lens in front of the slit they came from (of course all this talk about which slit a photon came from in a quantum experiment is suspect, but I think you can understand this as something like shorthand for which paths contribute significantly to the final outcome in a path integral).
  8. Apr 7, 2008 #7
    Thanks Jesse!

    On the first comment, there is still some uncertainty in position of the photons coming out of the entangled photon source. I found this paper on Beamlike Type II SPDC, which explains how the photons make a "blob" of coherent light rather than a cone of random photons like in normal SPDC:


    And as you say, as long as the source is far enough away from the two apparatuses, we should be able to assume a fairly straight direction - but not so perfect that we lose position certainty. :) Of course the formal experiment will have to take this into account.

    On the second, my response is to look at the Dopfer experiment. The detector at the focal point has some finite size - it's not a point. Yet the interference pattern generated is close to perfect. Which indicates to me that there is a small amount of wiggle-room here in terms of being exactly on the focal point versus being a millimeter or fraction thereof away from it. In other words, yes, passing through the focal point ensures a collimated beam, but passing very close to the focal point results in a photon that is very close to being parallel, if not perfectly so, which, when it strikes the third lens, may still strike the detector.

    Further, when the detector D1 in Dopfer is placed between the focal plane and the imaging plane we start to see a slow transition from a Gaussian pattern to an interference pattern, indicating further to me that we don't need perfect accuracy to get the interference pattern - only enough to make the maxima and minima significant enough to be detected outside the margin of error.

    What the experimenter must do (i.e., what I'd better do if I want this to result in anything useful :)) is to do the math and figure out how much wiggle room there is. If 90% or so of the photons whose twins pass through the slits in the bottom half wind up striking the detector in the upper half - heck, if 50% of them do - we should still see something resembling an interference pattern in the lower half.
    Last edited: Apr 7, 2008
  9. Apr 7, 2008 #8


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    What does the interference pattern have to do with it, though? You'd predict an interference pattern in the double-slit experiment even if you explicitly assume the slits have a finite width. I thought we were talking about the issue of whether 100% of the photons that were detected on the bottom apparatus would also have corresponding hits in the focal plane of the large lens.
    Well, by making the detector behind the large lens in the upper apparatus wider than a point, you open up the possibility that even though there'd be interference in the subset of photons in the lower apparatus whose twins went to a particular position in the upper detector's range, the total pattern of photons in the lower apparatus wouldn't show interference because the sum of all these subsets would be a non-interference pattern. In this way complementarity could be preserved without opening up the possibility that the total pattern at the lower apparatus would vary depending on what happened at the upper apparatus. I thought your argument critically depended on the idea that all the photons in the upper apparatus would be detected at a single position, so there'd be no way to mark out subsets of hits at the lower detector corresponding to distinguishable subsets of hits at the upper detector, and thus no way to have the total pattern of photons at the lower detector show non-interference without violating complementarity.
  10. Apr 8, 2008 #9
    Yes, the interference pattern in the bottom half reflects the superposition of many interference patterns of subsets of photons. But as we see in Dopfer, if those photons are detected only a short distance from the focal plane, those interference patterns will only be slightly out of sync with one another, resulting in the near-perfect, but not totally-perfect, pattern we see when D1 is moved slightly away from the focal plane, and then we see the pattern continue to morph into a gaussian pattern as D1 is placed further away.

    That is the only explanation of how Dopfer gets an interference pattern by placing the detector D1 - which is wider than a point - and keeping it fixed there. Yes, if D1 were _very_ wide, the pattern of photons in the lower half would be totally Gaussian, but like I said, there must be a margin of error for Dopfer's experiment to have worked at all, and I think the key to understanding it is to look at how the pattern slowly morphs as D1 is moved - otherwise, if what you're saying is right, we'd expect either a perfect interference pattern when D1 is at the focal point, or none at all as soon as D1 is moved a wavelength away.

    My hypothesis is that the photons that are slighly off from the focal point will make an interference pattern that is slightly out of phase with the "central" one. Indeed, the wider the detector D1 is, the more of a problem this will be.
  11. Apr 8, 2008 #10
    Here's a picture of what I'm talking about. At the focal plane, the perfectly collimated beams pass perfectly through the focal plane. Photons that are slightly astray still come very close to the focal point. As long as all photons are detected there the interference pattern should resemble that of Dopfer's.

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