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PDC Type I: 1+1=3?

  1. Sep 25, 2008 #1


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    EPR defined a form of realism which later figured in Bell's Theorem. If the outcome of a particle's observation could be predicted with certainty, then the observable had an "element of reality". In Bell tests, that is usually given as photon polarization. We see the so-called "perfect" correlations in which Alice and Bob, when observed at the same polarization angle, always give perfectly correlated (or anticorrelated) results at any given angle.

    The normal method of getting these results is to use PDC crystals, either Type I or Type II. Type II crystals yield anti-correlated photon pairs, while Type I yield correlated pairs. There is an interesting wrinkle in Type I pair generation, and this is what I have questions about.

    It takes 2 perpendicularly oriented Type I crystals to yield a polarization entangled stream of photon pairs. A single Type I crystal provides an output stream of known polarization, perpendicular to the input source. This stream, by itself, does not yield perfect correlations that would match the EPR definition of having an element of reality at any chosen observation angle.

    When the input stream is V>, The output stream is H>H> which does not lead to perfect correlations. If the crystal is rotated 90 degrees: the input stream is now H>, The output stream is V>V> which still does not lead to perfect correlations. If there are 2 perpendicularly aligned crystals whose streams are mixed suitably, we end up with a superposition of H>H> + V>V>, which is a good Bell state and the perfect correlations appear. This is how Type I crystals are used in actual Bell tests.

    So it seems to me that what we have here is 1+1=3. Suppose we had 2 completely independent lasers driving 2 completely separate - but perpendicular - Type I PDC crystals. The pair output of these setups would individually not be in Bell states (i.e. no perfect correlations). But if there are suitably combined in such a way that the source apparatus cannot, in principle, be determined, then the combined beam becomes a good Bell state. And it now passes the EPR "element of reality" test. Yet, clearly the photon pair came from one or the other of the two crystals, which did NOT pass the "element of reality test" individually. So the photon pair must have picked up "something" from the presence of the other crystal, even though nothing came from there. That's unreasonable!

    My conclusion is that "elements of reality", if they exist, are unreasonable. Am I crazy? I guess what I am saying is that any mechanistic picture of what is going on will always fail, even though the formalism works fine.

  2. jcsd
  3. Sep 26, 2008 #2
    Do you have a link or source that details a bit about how Type I PDC need to be fabricated I did not know it required two crystals to make them useful.

    The mostly I want to be sure I’m understanding how the Type one crystal works. If one produces paired photons but the fail to retain “entanglement” characteristics. But putting two in series allows one to down convert V inputs and the other H inputs each must be having some effect on the down converting photons produced by the other in order to gain the “entanglement” characteristics lost when only one was used. Do they explain any requirement to avoid any gap between the two crystals or can they be stacked with some distance between them. Any reference that gives some more detail on how the Down-converters need to be fabricated would be helpful.

    As to separating the two required Type I crystals into two separate source beams – I’d assume that both are required by each photon to build the full “entanglement” characteristics -- so the approach your suggesting should not work. That is gaining the “entanglement” part is a 1+1 = 2 crystals required in a beam to work.
  4. Sep 27, 2008 #3


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  5. Sep 28, 2008 #4
    Interesting. I wonder if someone has documented the correlation failure results of using just on crystal. I’m wondering if it tracked with the Classical 25% to 75% probabilities at the limits, Or if it tracked with the Bell limits of a straight line 100% to 0% ie. failing to cross that line.

    I was under the impression that the type II DC not only required two crystals, but need an optimal non-orthogonal alignment wrt pump beam for the separating cones of light to overlap usefully.

    I’ll have to look for more on how SPDC units are put together.

    DrC, did you understand my comment on "1+1 = 2 crystals" may be required to build a “good Bell state” so that the individual photons actually go through both crystals?
  6. Sep 28, 2008 #5


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    Well, they go through both crystals but only one physically acts on each photon/pair. Just as with the double slit, the possibility of going through either slit gives rise to the interference pattern... with the 2 crystals you get entanglement.

    I cannot say for an absolute fact that you could build the Bell state from combining 2 separate source lasers and separate crystals... but I assume it is possible to create such a superposition. Anyone out there know more?
  7. Sep 29, 2008 #6
    NO I disagree;
    In the double slit we are forced to consider that possibility of using both.
    Both with the 2 crystals there is no chance of any photon not being under the influence of both crystals. If the 1st one causes the down conversion both photons a must go though the 2nd subjecting them to some unseen adjustments. But if the 2nd one causes the down conversion it cannot have received the one photon without it having gone through the 1st where it could be subjected to some unseen preparation before down conversion.
    Those would be local and realistic effects not the same as a non-local second slit. Hence my 1+1 = 2 crystals required.

    I must say it is a little disappointing not to be able to find more data on exactly how tests on one crystal do not produce Bell volitions. It would be nice to know which of the Local-Realistic interpretations it matched best, the inequity line or the 75% to 24% line.
  8. Sep 29, 2008 #7


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    As far as anyone knows, the presence of a second Type I crystal does not affect the down converted output photons (or the source input photon). The crystals send the output photons "off angle" in cones. They are collected in areas in which the output cones overlap sufficiently that the source crystal cannot be determined. This combination leads to the H>H> + V>V> superposition, and thus the Bell state.

    There is nothing - from a QM perspective - needed to explain this result in the way of some interaction between the 2 crystals. But I do think there is a problem explaining what happens from a deterministic perspective. I.e. if you accept Bohmian/dBB explanations, you do need there to be something "extra" going on because there is no entanglement from either one individually, and yet this stream purports to be deterministically splitting at either one or the other of the crystals.

    Type II crystals, on the other hand, work very similarly but do not rely upon a superposition of 2 output streams to get a Bell state. They send out H>V> + V>H> directly, which is entangled.
  9. Sep 29, 2008 #8
    You are missing the point.
    Example: Using one beam with a HH crystal in the first position you can select two beams and get HH but there is no “entanglement”.
    Likewise with only the second slot filled with a VV crystal. The same two beams selection gives VV output one V in each beam but again you are reporting no measurable entanglement is observed.

    But you are reporting entanglement when both HH and VV are outputted by using both crystals.
    You also know the change cannot be due to any H reacting to a V because they never come through together by design of the experiment.
    But to you did change how the photons were prepared before detection and the change was a local one. The pair of HH photon was prepared with additional filtering through a VV crystal after DC.
    And the VV pump photon was pre-filtered by a HH crystal before DC.
    You cannot even claim it something like the Moon is not really there until I see or measure it somehow. Because you did observe the action of the added filter, with no entanglement observation before changing to entanglement observed after adding the extra filtration.
    From a QM perspective – Copenhagen requires the preparations be well accounted for; obviously the QM formula would reduce to 1+0 crystal = no entangle vs 1+1 = entangle.

    I don’t understand your Type II comments – the diagram on your own web pages show 2 output streams.
  10. Sep 29, 2008 #9
    1. I don't understand why an "element of reality test" requires entangled photons. If the output photons are not correlated (entangled) that means that some angular momentum has been transferred to other particles in the crystal. The conservation laws require that. If you could measure the spin of all particles in the crystal + one of the emitted photons you could certainly predict the spin of the other photon, so it is "real".

    2. You say that nothing came from the other crystal. This cannot be true because that crystal contains charged particles. And charged particles produce a field. The field of a single crystal is different from the field produced by two crystals. Nothing unreasonable about that. One planet goes straight. Another one goes the same. Both of them go round and round. Is this another case when 1+1=3?

    I think that by "mechanistic picture" you understand only billiard balls going straight and bumping into each other. Did you consider the hypothesis that each quantum particle can be accompanied by a classical-like local field and therefore interact with other particles without a direct collision?
  11. Sep 29, 2008 #10


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    I am not sure that an "element of reality" test requires entangled photons. EPR states that if the result of an observation can be predicted with certainty, there is an element of reality to that which is observed. Clearly, entangled photons can be used to create such a scenario.

    As to the field produced by 2 crystals: essentially, I am saying that the 2nd crystal produces no tangible effect. Of course it produces something, but so does air and that does not create a Bell state. I think the effect can be demonstrated without 2 crystals in series, but I am not certain about that.
  12. Sep 30, 2008 #11
    You could, in principle, predict the spin of a photon comming from a light bulb by measuring the spin of the atom before and after the emission. So, the spin of any photon is as "real" as the spin of an entangled one. This experiment is, however, experimentally unfeasible.

    1. It certainly produces a "tangible effect" because the experimental result shows that. So, it is not a question of "if" but of "how". The most probable answer is IMHO that the particles inside both crystals produce a field that influences the emission process.

    The air should, indeed, influence the emission but because the motion of air molecules is random, this effect is indistinguishable from noise.
  13. Sep 30, 2008 #12


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    That was essentially the EPR argument, they did not know that Bell states existed at the time. Quite the opposite, they assumed that the Heisenberg Uncertainty Principle was incomplete.

    At any rate, here is a question:

    Take a laser source, run it through a Polarizing Beam Splitter (PBS) so we have 2 separate output streams, H> and V>. Take the H> stream into a PDC crystal and get V>V> out, and take the V> stream into a second PDC crystal and get H>H> out. Now, recombine the 4 output streams so that you end up with 2 streams which will now be H>H> + V>V>. This is done in such a way that the path taken cannot, in principle, be determined.

    Will the resulting output streams be entangled in a Bell state? I am saying it will, and that the 2 crystals do NOT need to be in series to create a Bell state.
  14. Sep 30, 2008 #13
    I don't understand how you can claim that. It can only be an unfounded assumption what can support it?
    Your own observations contradict it.
    You shown us that same total number of photons produced by the two crystals separately are still produced when used together. But when used together they produce an observable change when you measure them - entanglement. You do consider entanglement a tangible observation right - and the only local change that could be causal is the inline second crystal. (I.E. 2 crystals DO NEED to be in series to create a Bell state).

    Also, from earlier you said:
    “When the input stream is V>, The output stream is H>H> which does not lead to perfect correlations. If the crystal is rotated 90 degrees: the input stream is now H>, The output stream is V>V> which still does not lead to perfect correlations.”

    The comment (the input stream is now H>,) is incorrect - rotating the crystal does not change the input stream alignment only the alignment of the crystal wrt it. There is no evidence a crystal is sensitive to the polarization of the input stream, in fact the paper you provided in post #3 shows a polarizer in the source beam (fig 1); yet both crystals do their job the same. The only thing controlling the output alignment is the crystal not the input stream. The results give no indication as to what the alignment of a Pump Beam photon may have been.

    I also found something I’d not seen before:
    Table 1. there shows both a type I & II UP CONVERSION (?) of 1064nm to 355nm using a Third Harmonic .
    That is three photons becoming one!

    Yikes; how does a BBO do that?
  15. Sep 30, 2008 #14


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    The crystals are definitely sensitive to the polarization of the input stream. Only 1 polarization (either H> or V> depending on orientation) is supported by Type I crystals. That is why you need 2 oriented orthogonally to get a Bell state. Usually the pump input laser is oriented at a 45 degree angle so that half of the input is H> and half is V> (randomly). So half acts within one crystal, half in the other.
  16. Sep 30, 2008 #15
    Ok I can accept that;
    but it still only says that the V photons are not converted by a H crystal.
    That does not mean the H crystal cannot modify V photons in a way that can only be detected by a V crystal producing “entangled” photon pairs it could not otherwise produce.
    The observations you’re pointing out supports that the H crystal do modify V photons that way and therefore; 2 crystals DO NEED to be in series to create a Bell state.
  17. Oct 5, 2008 #16
    Bell states are not different in this aspect. It is just momentum conservation, which always holds. You can always predict the spin on a certain axis in the way I said. In order to see a problem for realism you need a supplementary assumption, that the spin of the entangled particles, on any axis, remains the same regardless of how you measure it. This assumption only makes sense in a naive, billiard-ball interpretation. Even for a classical field theory such an assumption is wrong. The trajectory of a particle depends of the configuration of other particles around it.

    You are probably right. But how does this new setup affect my argument? You still have different matter configurations leading to different experimental results.
  18. Oct 6, 2008 #17


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    Sorry, in the exchange I lost the sense of what you are asserting. I don't dispute that there are a variety of ways of express entanglement and/or conversation laws besides PDC photon pairs. But they produce Bell states that have 2 important properties: they display the "perfect" correlations when measured at identical settings, and they violate Bell inequalities at specificied other settings.

    On the other had, the individual streams of Type I PDC crystals show neither of these qualities. yet when 2 output streams are combined, each photon pair emerging individually gains the Bell state attributes. Now, how can a mechanical explanation provide an answer in this case? I say that the QM formalism does precisely because it is *silent* on the mechanics and does not insist on "realism". On the other hand, any realistic explanation - even non-local ones - are going to have a severe problem here. I would propose that any non-local mechanical hypothesis be required to explain this Type I PDC paradox satisfactorily without resorting to the familiar "My theory always gives the same answers as QM" mantra.

    Once again, the paradox is: A single particle pair emerges in a Bell state ONLY when the output of 2 PDC crystals are combined, even though that same particle pair must emerge from the source PDC crystal *without* being a Bell state. The presence of the 2nd crystal, from which the pair could not have emerged, does nonetheless figure into the emergence of the Bell state. In a deterministic theory (as BM/dBB claims to be, for example), it must have gone through one or the other and not a superposition of both. So I say that BM/dBB cannot truly claim to be a deterministic theory and still provide an adequate explanation of this paradox.
  19. Oct 6, 2008 #18
    PDC Type I: 2 together or seperate & combined

    I disagree with ueit; I still think you are probably wrong.
    First on the point made:
    “On the other hand, the individual streams of Type I PDC crystals show neither of these qualities.”

    Exactly what plot is produced by using a single Type I PDC crystal; lets say where A is held to a measurement at 45°. What would the observed plot at B from 0° to 90° show, do we have anything where someone has published actual observations for something like that?

    Second: A
    “Bell state ONLY when the output of 2 PDC crystals are combined”
    Is not what is happening. Experiments that show the Bell State do not “combine” outputs – the outputs are overlapping there is a difference. Your set up is the plan that requires combining separate beams for two separate crystals not stacked.

    “Now, how can a mechanical explanation provide an answer in this case?”
    Easy and I already have.
    Neither of the independently created but overlapping beams can avoid going though the crystal that not responsible its down conversion at some local point either before or after the DC. Therefore the experiment does not eliminate the possibility of some unknown hidden local[/] influence on the individual photon parameters as they pass through the other crystal.

    Your modified test (do we know if any one has actually thought to try it) does remove the possibility of any individual photon from being modified by both crystals. Since yours would eliminate any chance of some hidden local influence I predict such a test would fail to produce Bell correlations by combining the two beams.

    So the question is – if your set up did fail to produce a Bell State – would that be seen as support for some realistic local influence?

    Unless an experimenter though it would, there is probably little point in doing the experiment.
    I doubt there would be much interest in trying it – I suspect QM experts would say even QM expects the, two beam split and then combined, plan would fail to produce a Bell State.
  20. Oct 7, 2008 #19


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    Re: PDC Type I: 2 together or seperate & combined

    1. With 1 crystal of Type I, the output polarization is known. If the input was oriented to H>, then the output is V>V>. This is not an entangled state, so you won't see the perfect correlations except at the known spots: V> or H>. I think the general formula is:

    C = (cos^2(A) * cos^2(B)) + (sin^2(A) * sin^2(B))

    This is the same formula as any 2 vertically aligned photons, having no other connection. Unlike with entangled photons, this does not reduce to a formula which has theta as the only variable.

    2. Yes, the 2 cones overlap (one cone for each crystal). But the overlapping cones do make for the combination of the output stream, and it is done somewhat for convenience. It makes it easier to collect and merge the streams into a single stream. Here is a quote from the authors (actually from a companion piece - emphasis added):

    "A given crystal can only support Type I downconversion
    of one pump polarization, the other polarization
    simply passes through the transparent crystal
    . Our source uses
    two identical crystals, with one rotated 90◦ from the other
    about the beam propagation direction, as shown in Figure 2.
    In this arrangement each crystal can support downconversion
    of one pump polariazation. A 45◦ polarized pump photon
    can downconvert in either crystal, producing a polarization entangled
    pair of photons"
  21. Oct 7, 2008 #20
    Re: PDC Type I: 2 together or seperate & combined

    That doesn’t make sense! Given two correlated beams with only VV and holding A @ 45°. Wouldn’t this give a plot of correlations with B going from 0 to 90° of 50% at all angles. There shouldn’t be any photons detected at 90° by B.
    More important, What has actually been measured for real!

    Yes I understand that is what is claimed – that’s the whole point.
    What is offered as proof no hidden effect is happening as they simply passes through the other transparent crystal?
    Do you think your set up might give that proof?
    1.) What do you think the meaning would be if you do build a Bell State by combining four beams into 2.
    2) What do you think it would mean if your set up fails to produce a Bell State by combining four beams into 2.

    Would that failure mean that when photons simply passes through the other transparent crystal something local but unknown must be happening we are not aware of, that contributes to building the Bell State?
  22. Oct 7, 2008 #21


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    Re: PDC Type I: 2 together or seperate & combined

    1. I should have made clear:

    C = (cos^2(A) * cos^2(B)) + (sin^2(A) * sin^2(B))

    where C represents the correlations, either both detected as V or both detected as H.

    2. I think if there was something added by the second crystal, that would have been noticed years ago. The Type II PDC crystals produce an entangled state using just one crystal, the reason being that the output varies between H>V> and V>H> when a 45 degree pump input stream is applied. The Type I crystals produce a single polarization, so they can do that. So I don't think there is much likelihood of there being something missed. But my proposed setup might make that more clear.
  23. Oct 8, 2008 #22
    Re: PDC Type I: 2 together or seperate & combined

    So to be clear for a single crystal are you claiming?
    C = (cos^2(A) * cos^2(B))
    Somehow that does not seem right, but what counts are actual observations. I’m assuming someone has, what I’ve not found is where such observations of correlations using a single crystal have been published.

    But we have noticed for years that the Bell State is addded! It only appears when there is the opportunity for “something added” by a second crystal in close enough alignment to cause overlapping. I’ve seen nothing to make clear that is not the case.
    Maybe; If so, it could be a very important experiment and from what I see easily within the capabilities of an undergraduate program as described it the paper you have referenced. But before having someone actually do even a relatively easy one (as quantum tests go), there hould be a clear statement as to the meaning of each of the two possible outcomes (Bell State or No Bell State) of the experiment as I asked.
    Do you have an idea of what you would conclude if the results were not as you hope and no Bell State was found? Would you only accept reality as "local"? If not what's the point in doing the test?

    I would think a physics program able to do such a test such as University of Texas at Austin or University of Illinois at Urbana-Champaign would most value doing experiments where different outcomes will support different conclusions about existing assumptions.

    Personally, I would love to stake our differences on the outcome of your proposed experimental setup with no option to change our minds if the experiment does not go my way. Bell State produced as you propose - Non-Local Reality confirmed - and I’ll never question it again. Or Bell State not produced - Local Reality confirmed - and you never dispute it again.

    But as a Local Realist I feel I’d be taking advantage;
    Because I’m convinced the real experts in Texas and Illinois would use QM, prior to running the experiment, to predict No Bell State for your experiment. And I think they would even add that if your experiment did produce a Bell State they would, in advance of seeing such a result, state that it would mean either a serious problem with how QM is defined or that something was wrong with the way the test was preformed.

    Of course if you check with the experts and I’m right about what they would predict -- it kind of knocks the wind out of any need to do the experiment since QM & LR predict the same thing.

    Are you sure about that? I know polarizing beam splitters are not just one prism but two joined together. I was under the impression that some (maybe all) Type II PDC devices were also made of two special cut crystals joined and aligned at a certain angle wrt the incoming beam to get the two output cones to overlap as needed. I’m not sure how to confirm the actual fabrication of a Type II PDC.
  24. Oct 8, 2008 #23


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    Re: PDC Type I: 2 together or seperate & combined

    The term you provided is only for the H>H> match. The sin^2 term is for the V>V> match as well. You add them to get the total correlations (matches). The reason you haven't seen it published anywhere is that the result doesn't add to our knowledge in any way. The output of a single Type I PDC crystal is not entangled and that is the interesting side of things. I am sure that experimenters have noted this result many times as they perform alignment and other tests as part of a "normal" Bell test using 2 crystals.

    On the other hand: The proposed setup does *not* test local reality. It is just a way to highlight the difficulty with mechanistic explanations. QM says, in effect, 1+1=3. But a mechanical explanation - one which purports to describe what is going on in physical (and not just mathematical) terms - will have problems with this treatment.
  25. Oct 8, 2008 #24


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    Attached is a diagram of the proposed setup. In this setup, the Type I PDC crystals are in parallel rather than their normal series alignment.

    I realize it might be difficult to achieve this arrangement in practice, as the paths must be precisely setup so that the path taken cannot be determined. Care must be taken that there is no destructive interference as well.

    Attached Files:

    Last edited: Oct 8, 2008
  26. Oct 8, 2008 #25


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