Delayed Choice Bell-state Quantum Eraser

[Cthugha]

I think at this point it might be a good time for you to summarize your conclusions / beliefs / concerns about the experiment in general. Your beliefs regarding my two points of interest mentioned above are obviously what I am most interested in hearing about, but anything else noteworthy is welcome also. Please use the least technical language possible and cite supporting references if possible (even in the German document).

Ok, it might be a bit early in the discussion for the final conclusion, but let me discuss some points that might lead to a better understanding and solve the issues.

At first, I have to point out the spatial coherence topic again as it is most central to any double slit experiment. However that point is somewhat underplayed in basic discussions of the double slit experiment. See for example the following discussion from a different topic in these forums:
https://www.physicsforums.com/showthread.php?t=428319"

Note especially the posts by Andy Resnick, explaining the importance of coherence for any interference pattern and the notion of spatial coherence being a measure of how point-like the source is.

I hope you are familiar with the physics behind the double-slit, but let me paraphrase it. As you are not a scientist, I just want to be sure we are talking about the same issues. The interference pattern arises due to the two fields originating from the two slits. The intensity at any point is given by the squared sum of these fields. As the fields have a phase, those fields can cancel out at a certain position (phases are opposite) or they can add up (equal phase) or anything in between. Now the important point is that these two fields at the slit originate from one common field: The light source placed somewhere in front of the slits. The field from this source travels to the two slits and there is some fixed phase difference between the fields at the slits, which is determined only by the geometry of the experiment. As the phase of the field varies in a sinusoidal manner with the distance between the source and the position of interest, you can calculate the difference between the phases at the two slits without knowing the initial phase at the source. The difference at the slits does not depend on that. This would not work if you used two light sources and placed them in front of each slit. As there is no fixed phase difference between these sources, you will also not get a fixed phase difference at the slits and therefore also no interference pattern.

Now the important point lies in remembering that only the geometry determines the phase difference at the slits. If you consider real light sources, they are not point-like, but have a finite size. Now you can calculate the phase difference at the slits again for a point on one end of the light source and one point on the other end of the light source and will notice that they are slightly different. The phase difference at the slits becomes less well defined and so does the phase difference of the two fields originating from the slits. The interference pattern will become a little bit less visible. What a normal double-slit experiment really measures is exactly the spread in these possible phase differences which can occur at the slit. Basically this is spatial coherence. Maybe it might help if you make a simple sketch of the different situations yourself. It is not really complicated.

To sum up, you need indistinguishable fields originating from two positions with a fixed phase relationship to see an interference pattern. Now there are two possibilities hot to not get such a pattern. You can either not have such a fixed phase relationship (lack of spatial coherence) or you can have distinguishable fields by providing which-way information.

These basics are both necessary to understand the remaining physics behing two-photon interference and DCQE experiments. Was my line of reasoning somewhat clear or should I try to explain it differently? Up to now there is nothing too mysterious involved. This is stuff from a basic optics course. If that point is clear I can continue to tackle the entanglement.

 

[Kyle-DFW]

I assume that the field to which you are referring is an electromagnetic field and that at this point we are describing photons as waves passing through the electromagnetic field?

If so, then yes, I think I'm following you. Are you or are you not in agreement with the idea that even a single photon is a wave that can go through both slits simultaneously?

What is your explanation for the perceived collapse of the photon to a discrete location in space (when it seemingly becomes a particle)?

Do you have an explanation for the retro-causality?

 

[unusualname]

Cthugha,

I suggest you link to a reliable source that confirms the relevance of your arguments to the interpretation of this experiment. Since it was published in a respected peer-reviewed journal I would not expect such obvious and sloppy details to have been overlooked if they were relevant.

It is possible that the experiment has faults, but can you point to arguments other than those posted on this forum that confirm this? (to avoid appearing to be an obsessive "loophole hunter")

cheers

 

[Joseph14]

Cthugha,

I suggest you link to a reliable source that confirms the relevance of your arguments to the interpretation of this experiment. Since it was published in a respected peer-reviewed journal I would not expect such obvious and sloppy details to have been overlooked if they were relevant.

It is possible that the experiment has faults, but can you point to arguments other than those posted on this forum that confirm this? (to avoid appearing to be an obsessive "loophole hunter")

cheers

What is your interpretation?

 

[unusualname]

What is your interpretation?

QM is non-classical, nature is non-local, non-real or both

 

[Joseph14]

QM is non-classical, nature is non-local, non-real or both

Sorry I meant interpretation of this experiment. I've listed the 3 main senarios below.

1. No polarizer at A and no quarter wave plates at B------Interference
2. No polarizer at A and quarter wave plates at B---------No Interference
3. Polarizer at A and quarter wave plates at B------------Interference depending on angle of Polarizer

Also how is your interpretation different then Cthugha's?

 

[Cthugha]

Everytime this experiment comes up for discussion Cthugha posts the same old argument about how it's important to consider spatial coherence etc, completely missing the point of the experiment which is to demonstrate the seemingly bizarre "retrocausal" nature of QM. The explanation is to adopt your preferred "interpretation" of QM and note how it consistenly explains the results without requiring "retrocausality" (except perhaps in the transactional interpretation).

Yes, and I will do so time and again.

Of course you can explain this experiment using any interpretation you like. All I am doing is pointing out where the mysterious phenomena are indeed found and where not. I will place some more details in the reply to the next few sentences.

Cthugha seems to suggest that a classical optics type explanation can be adopted, otherwise I don't understand the constant highlighting of irrelevant issues. A small area detector is used because an alternative reliable wide detector wasn't available that could accurately match coincidences between idlers and signals (or maybe a fancy CCD was too expensive)

Well, just using a movable detector would not be that difficult, would it? In fact, the other famous quantum eraser experiment, the one by Kim et al., indeed shows that the position of that detector matters. They place the movable detector at the experiment side without double slit and still see changes in the coincidence counts as they move the detector on this side around. Also I am not saying that a classical explanation is possible. I am just distinguishing between all the points that can be explained classically and those which cannot. The basic prerequisite for seeing an interference pattern in any double slit experiment in the world is always spatial coherence. The non-local way of retrieving spatial coherence and WW info (or not) by performing measurements on separated entangled photons is the "magical" non-classical quantum part. What makes it really look paradoxical is the (not really present) choice to keep or destroy the interference pattern after one of these photons has already been detected. Any way of explaining this without retrocausality must necessarily include some kind of subsampling. Although you might consider it a minor point, spatial coherence is needed at this point to explain, why you would never see an interference pattern in the detection at the idler side alone, without doing coincidence counting, even if you had detectors of ideal efficiency. You need to explain this using different subsamples leading to different coincidence count interference patterns which sum up to a simple Gauss peak.

Also I am explaining the need to use coincidence counting. Laymen asking questions about this experiment on these forums often do not even notice that the interferences are only visible in coincidence counts, which tells me that this point is not intuitively clear.

However, I agree that the issue of detector size would not matter if you had polarization entangled photons with extremely well-defined momenta, but this is (up to now) not the case in real experiments.

The experiment is a beautiful demonstration of the non-classicality of QM. Appealing to an obscure german phd thesis or classical arguments involving coherence is just obscuring the simple message

Obscure German thesis? Zeilinger and his PhD student are obscure guys? Oh, come on. You can't be serious. Zeilinger even cited this thesis in his famous "happy centennary, photon" review article posted in Nature. IMHO these popular-media discussions about retrocausality obscure the real physics contained in the experiment: Complementarity is very fundamental.

I suggest you link to a reliable source that confirms the relevance of your arguments to the interpretation of this experiment. Since it was published in a respected peer-reviewed journal I would not expect such obvious and sloppy details to have been overlooked if they were relevant.

I am a bit puzzled. I do agree with all what is claimed in the text by Walborn et al. as they do not claim to have evidence for retrocausality or such. This is explicitly stated in the DCQE paper and also in their review paper I linked below. I even strongly agree with their conclusion that complementarity is fundamental. I do indeed disagree with many of the popular media versions of this experiment that claimed that this experiment was a clear demonstration of retrocausality and such stuff. Most popular websites on the net dealing with this experiment adopt this erroneous line of reasoning. Even wikipedia links one of these crackpot pages. And while the notion of spatial coherence is trivial and perfectly well known to anyone doing actual research in optics - this is treated in a basic optics course - I am quite sure most of the laymen who have seen crackpot sites on the net are not familiar with it. And in my opinion spatial coherence gives the best link to subsampling and complementarity as spatial coherence is directly linked to having momentum eigenstates, which elegantly underlines the need to destroy which-way info.

I assume that the field to which you are referring is an electromagnetic field and that at this point we are describing photons as waves passing through the electromagnetic field?

If so, then yes, I think I'm following you. Are you or are you not in agreement with the idea that even a single photon is a wave that can go through both slits simultaneously?

Yes, I agree with you.

What is your explanation for the perceived collapse of the photon to a discrete location in space (when it seemingly becomes a particle)?

If I knew that for sure, I would get a lot of prizes, I suppose. There are a lot of interpretations allowing this to happen, but I do not know of any evidence for one being better than the other. I do not know the correct answer.

Do you have an explanation for the retro-causality?

Yes, but as I am lazy and it is getting really late here, you might also find the explanation in this review article easier. By the way it is written by part of the authors who actually wrote the paper we were talking about:
http://www.fsc.ufsc.br/~lucio/2003-07WalbornF.pdf"

 

[unusualname]

No it doesn't show retrocausility, that's correct, it shows that you need a non-classical interpretation of nature such as one of the well-known "interpretations" of QM.

I really don't understand what you see as so important to address here. Are you passionately worried that the world is being misled by the results of the experiment? Does analysing every point of it suit any purpose? There are quite a few other experiments (including by Zeilinger) which demonstrate the non-local or non-real nature of QM, the evidence is pretty overwhelming. If this one has some obvious "loopholes" then write to phy. rev. and have your concerns published.

Your points are fussy and trivial like the loophole problems people bring up wrt the Aspect experiment. Experimenters just extend the distances, improve the detection, improve the photon sources etc etc and QM non-classical nature stands firm.

I think there should be a subforum for tediously analysing possible loopholes in QM experiments where you guys can argue the little details over pages and pages.

Bohr did these experiments in his head in the 1920/30s and pretty much arrived at the correct conclusions.

What is the important point you want to make? The delayed choice QE is a beautiful confirmation of QM and why classical theory can't explain nature, isn't it?

 

[Joseph14]

I really don't understand what you see as so important to address here. Are you passionately worried that the world is being misled by the results of the experiment? Does analysing every point of it suit any purpose?

The point about detector size actually cleared something up for me about the coherence of entangled sources. That is probably why Cthugha posts useful insights like that to help people with questions.

What I don't understand is why you show up here with absolutely nothing to contribute and try to put words in people mouths. No one here is trying to find loopholes to avoid accepting QM or trying to explain QM by classical mechanics, but you have been going on about that incessantly.

 

[Cthugha]

I really don't understand what you see as so important to address here. Are you passionately worried that the world is being misled by the results of the experiment? Does analysing every point of it suit any purpose? There are quite a few other experiments (including by Zeilinger) which demonstrate the non-local or non-real nature of QM, the evidence is pretty overwhelming. If this one has some obvious "loopholes" then write to phy. rev. and have your concerns published.

I am now even more puzzled. I do not claim that there are any loopholes. It is as non-classical as any other experiment based on entanglement. I am perfectly fine with that manuscript. However, there are often questions which go beyond what is explained in the manuscript as they are trivial to the experimenters, but not to the laymen coming here.

What is the important point you want to make? The delayed choice QE is a beautiful confirmation of QM and why classical theory can't explain nature, isn't it?

What is the important point? Most discussions on DCQE in these forums are with laymen and in my opinion one should at least have an idea of the standard version of an experiment before discussing the non-local entangled version. It saves a lot of time which might otherwise be spent on misunderstandings. If you skip the spatial coherence issue you run into problems explaining why interference will never be seen in one arm alone. Because if you saw interference there, this would really mean retrocausality. A lot of people ask this question about why this coincidence counting is indeed necessary. And exactly that point is what I would like to be able to explain even to non-specialists. And this is where spatial coherence is needed. Although indeed trivial if you work in optics, it helps understanding a lot if you are just a layman. I am perfectly fine with the experiment and its conclusions, but it is not self-explanatory to laymen. So I just add the trivial points which are skipped in the paper. Not more.

 

[unusualname]

the last time I had a "discussion" with Cthugha about this experiment he seemed to be arguing that the coincidence counting was necessary to ensure "spatial coherence" or something similar, rather than trivially being necessary to just match idlers with their corresponding signal partner.

I couldn't understand him at the time and don't understand him now. This would be rather an important point to make clear in the paper if it was the case don't you think?

The only relevant details in this experiment are:

1) you get a recognisable interference pattern with coincidence matching if the eraser is in place
2) you don't if it is removed
3) the distance of the eraser can be greater than the distance to the signal detector

The details about classical coherence etc are not relevant in the Walborn setup, even though they may be in other versions of the delayed choice experiment. It is ~20 year old experiment. Much more sophisticated experiments have been performed to demonstrate even stronger non-classicality of QM since then.

The whole point of the experiment is that it can't be explained by classical optics. The coincidence matching is supposed to be a trivial mechanism for matching entangled pairs. Any other view is over-analysing, over-complicating and over-obscuring the experiment.

 

[Cthugha]

the last time I had a "discussion" with Cthugha about this experiment he seemed to be arguing that the coincidence counting was necessary to ensure "spatial coherence" or something similar, rather than trivially being necessary to just match idlers with their corresponding signal partner.

It is of course also necessary to match signal and idler.
However, if that was the only meaning, you would indeed run into problems when discussing what happens under ideal conditions. In a nutshell, my line of reasoning is as follows: You never see an interference pattern in one arm alone. This is generally accepted and ensures that no retrocausality is involved. Now one can adopt the point that the coincidence counting is just to filter background counts and the pattern would be there in one arm under ideal conditions. However, one can now discuss the case of ideal detectors and no background noise. You detect all photons at the idler side and all photons at the detector side without erroneous counts. However, you still should see no interferences in one arm alone. However, the patterns you get if you just take all detections at the double-slit side alone and the sum of all coincidence detections using ideal detectors should give you the same pattern. Both times you have detected all the photons at the double-slit side. Any difference between these cases would introduce retrocausality. Then this pattern should appear or vanish depending on whether you perform a position measurement on the other photon. This would allow retrocausality and ftl information exchange. Accordingly there must be some other reason why there are no interferences in one arm even if you have ideal detectors there. This reason is always some kind of subsampling. Generally speaking, you can in most cases use polarization subsampling (like explained in the review paper I linked). However, in the situation corresponding to figure 2 in the DCQE paper (all polarizers removed, still interference) you need some other kind of subsampling to ensure that even with ideal detectors there is no interference pattern in one arm alone. This is trivially assured when taking spatial coherence into account as (under the experimental conditions presented here) only a subsample of the total photons arriving at one side can show spatial coherence, while the total ensemble cannot.

I couldn't understand him at the time and don't understand him now. This would be rather an important point to make clear in the paper if it was the case don't you think?

No, I do not think so. Why should they discuss the cases of ideal or movable detectors if they do not use them? This is neither a heavy theoretical nor a pedagogical paper. The way they set up their experiment, spatial coherence in coincidence counting is automatically ensured. You also do not explain things like conservation of energy or how light propagates in such papers as they are research papers and not meant to be pedagogical. Accordingly I would also consider it strange to discuss spatial coherence in this paper as you expect a reader familiar with these concepts.

The details about classical coherence etc are not relevant in the Walborn setup, even though they may be in other versions of the delayed choice experiment. It is ~20 year old experiment. Much more sophisticated experiments have been performed to demonstrate even stronger non-classicality of QM since then.

I agree that there are other experiments where the connection to spatial coherence is more striking and more important, but I had enough discussions in these forums where the discussion took exactly the above "why is there no interference in one arm alone->what happens if we use ideal detectors" path, even for the Walborn experiment.

The whole point of the experiment is that it can't be explained by classical optics. The coincidence matching is supposed to be a trivial mechanism for matching entangled pairs. Any other view is over-analysing, over-complicating and over-obscuring the experiment.

I still tend to disagree. The question why there still is no interference pattern in one arm, even using completely ideal detectors, where there is in principle no need to perform coincidence counting out of noise reasons, is not that trivial, at least to "first-timers".

 

[unusualname]

Your ideal scenario doesn't exist, even if there is no background noise. QM is probabilistic, 50% of the idlers won't even pass through the polarizer, we can't ever know which will and which won't. The double-slit itself introduces an enforced "choice" on the signal photons, we can't know which slit they will pass through or if they will hit around the slits.

You can never, even in an ideal scenario with no background noise, do this experiment without coincidence matching. You would indeed have ftl signalling if such a scenario was possible.

The pattern in one arm alone will surely always be random noise.

So coincidence counting is required to retrieve an interference pattern due to the probabilistic nature of QM, not to ensure classical coherence of any sort.

 

[Cthugha]

This is exactly why I was referring to figure 2 of the paper. In this geometry there are no polarizers inserted at all and you still see the coincidence count interference pattern. The loss at the polarizer therefore clearly is not an issue here.

The loss at the double slits also is no problem as my intention is to compare the pattern formed by all photons exiting the double slit (without performing coincidence counting) to the coincidence count pattern between these photons and all photons detected under ideal circumstances on the other side. These patterns must necessarily always be the same and loss before the double slit is therefore not an issue as you do not consider these photons anyway in comparing these two kinds of patterns. As these patterns are necessarily the same (I am still considering the case without any polarizers), the only possibility to change the coincidence count pattern lies in not considering some of the photons on the "no double slit" side. As you also do not want to have position information present on this side, the photons will be in momentum eigenstates (or at least in states close to them). No matter how you arrange the experiment, photons with different momentum will arrive at a slightly different position in the detector plane at the "no double slit" side. Therefore disregarding some of them automatically means having a smaller span of momenta and therefore also increased spatial coherence. There is no way around that.

I mean - spatial coherence is exactly the quantity measured in double slit experiments. It would be really strange if it did not play any role wouldn't it?

 

[unusualname]

This is exactly why I was referring to figure 2 of the paper. In this geometry there are no polarizers inserted at all and you still see the coincidence count interference pattern. The loss at the polarizer therefore clearly is not an issue here.

The loss at the double slits also is no problem as my intention is to compare the pattern formed by all photons exiting the double slit (without performing coincidence counting) to the coincidence count pattern between these photons and all photons detected under ideal circumstances on the other side. These patterns must necessarily always be the same and loss before the double slit is therefore not an issue as you do not consider these photons anyway in comparing these two kinds of patterns. As these patterns are necessarily the same (I am still considering the case without any polarizers), the only possibility to change the coincidence count pattern lies in not considering some of the photons on the "no double slit" side. As you also do not want to have position information present on this side, the photons will be in momentum eigenstates (or at least in states close to them). No matter how you arrange the experiment, photons with different momentum will arrive at a slightly different position in the detector plane at the "no double slit" side. Therefore disregarding some of them automatically means having a smaller span of momenta and therefore also increased spatial coherence. There is no way around that.

I mean - spatial coherence is exactly the quantity measured in double slit experiments. It would be really strange if it did not play any role wouldn't it?

The role it plays is irrelevant in this experiment (Walborn). I think you are used to an analysing some of the older experiments where multiple paths were involved and in those cases your classical analysis does have a relevant role and is necessary to correctly interpret the results.

However I can't see how your arguments are relevant to the Walborn experiment, but I have stated my case as clearly as I have time for now, and you have at least made some detailed points which others might want to consider and decide for themselves whether they are relevant are not.

Like the last time I just want to say I have a different understanding of the role of the coincidence counter to you. I think we have both made our positions clear enough.

 

[Cthugha]

Sure, no need to let this discussion get too boring for the other guys reading this topic (well, if there are any left). As said before, I would perform that experiment myself if we had the equipment and time here, but although we have good photo diodes and a coincidence counting circuit, we do not have a suitable BBO for PDC here, only those useful for standard SHG. Maybe I can convince my boss some time that it might also be sensible to have a look at basic coherence issues instead of higher order ones again. However, I doubt that. Foundations of physics is not really a topic generating sufficient funding.

 

[San K]

Sure, no need to let this discussion get too boring for the other guys reading this topic (well, if there are any left). As said before, I would perform that experiment myself if we had the equipment and time here, but although we have good photo diodes and a coincidence counting circuit, we do not have a suitable BBO for PDC here, only those useful for standard SHG. Maybe I can convince my boss some time that it might also be sensible to have a look at basic coherence issues instead of higher order ones again. However, I doubt that. Foundations of physics is not really a topic generating sufficient funding.

Interesting discussion (i.e. on the DCQE). In the DCQE by Walborn...et al.In the below experiment the eraser is in the path of p-photon before s is detected.

Then s is detected and then p photon encounters the polarizer and then Dp.

If we were to insert the polarizer after s is detected, would the pattern/results change?...when compared to just keeping the polarizer in the path all the time...and not having to re-insert it after s has been detected (and before p reaches the polarizer)

Please see the link and the section referred to below:

http://grad.physics.sunysb.edu/~amarch/ Next the erasure measurement is performed. Before photon p can encounter the polarizer, s will be detected. Yet it is found that the interference pattern is still restored. It seems photon s knows the "which-way" marker has been erased and that the interference behavior should be present again, without a secret signal from photon p.

in summary:

does it matter if the eraser (or even the quarter plates or anything) is not in the path (i am Not saying encountered/reached by p) before s hits the detector? but put in the path of p after s hits the detector...(and a few milliseconds later the p encounters the polarizer...but all this happens after s has been detected)

i am trying to rule out the so called, hypothetical, pilot waves...

 

[San K]

Cthuga,

what is your take on the DCQE...i.e. the pattern on Ds matching
with
what we do with p (which-way or no-which-way) after s has registered its location on Ds?

are you suggesting that the "filtering" of photons happens in such a way that the pattern on Ds will match with what we do to p?

 

[San K]

I am now even more puzzled. I do not claim that there are any loopholes. It is as non-classical as any other experiment based on entanglement. I am perfectly fine with that manuscript. However, there are often questions which go beyond what is explained in the manuscript as they are trivial to the experimenters, but not to the laymen coming here.
What is the important point? Most discussions on DCQE in these forums are with laymen and in my opinion one should at least have an idea of the standard version of an experiment before discussing the non-local entangled version. It saves a lot of time which might otherwise be spent on misunderstandings. If you skip the spatial coherence issue you run into problems explaining why interference will never be seen in one arm alone. Because if you saw interference there, this would really mean retrocausality. A lot of people ask this question about why this coincidence counting is indeed necessary. And exactly that point is what I would like to be able to explain even to non-specialists. And this is where spatial coherence is needed. Although indeed trivial if you work in optics, it helps understanding a lot if you are just a layman. I am perfectly fine with the experiment and its conclusions, but it is not self-explanatory to laymen. So I just add the trivial points which are skipped in the paper. Not more.

Cthuga, you have a great point here, however I don't get it fully yet.

Even if we have zero noise there would be no interference pattern because we still need to filter out the photons that are spatially in-coherent?

how do we separate the coherent photons from the incoherent ones?

Is (neat clean) interference caused only between spatially coherent photons?

 

[Cthugha]

Even if we have zero noise there would be no interference pattern because we still need to filter out the photons that are spatially in-coherent?

how do we separate the coherent photons from the incoherent ones?

Is (neat clean) interference caused only between spatially coherent photons?

No, it does not work like that. Coherence (whether spatial or temporal) is rather a property of a state than of a photon. You can roughly translate it to "If I know the phase of my system at position/time A, with what probability can I predict it at position/time B". However, one can call this the property of a photon, if your system consists exactly of one photon or you have many photons, but they are statistically independent. While this is often the case,it is clearly not the case in DCQE experiments. This has been pointed out for example by Scarcelli and Shih ("Random delayed-choice quantum eraser via two-photon imaging", G. Scarcelli et al., Eur. Phys. J. D 44, 167-173 (2007) - also available on arxiv: http://arxiv.org/abs/quant-ph/0512207v2" ), where the following is said:

As for the entanglement, this experiment has strikingly shown a fundamental point that is often forgotten: for entangled photons it is misleading and incorrect to interpret the physical phenomena in terms of independent photons. On the contrary the concept of “biphoton” wavepacket has to be introduced to understand the nonlocal spatio-temporal correlations of such kind of states. Based on such a concept, a complete equivalence between two-photon Fourier optics and classical Fourier optics can be established if the classical electric field is replaced with the two-photon probability amplitude. The physical interpretation of the eraser that is so puzzling in terms of individual photons’ behavior is seen as a straightforward application of two-photon imaging systems if the nonlocal character of the biphoton is taken into account by using Klyshko’s picture.

While people seem to accept and expect deviations from statistical independence for fermions straight away - maybe because the Pauli exclusion principle is so famous - people often expect photons to be independent of each other, which is not that often the case. Even simple thermal light shows something like collective behavior. This is why it is quite often used for ghost imaging.

Therefore you do not need to consider the coherence properties of the individual photons - they are pretty incoherent and that is why you never see any interference pattern in one arm of the experiment alone - but the coherence properties of the two-photon state. In the case of spatial coherence, a coherent state means that the wavevector is well defined, while there is a broad distribution in wavevectors for a spatially incoherent state. Now spatial coherence for a single photon would mean that is has a sharp wavevector. Spatial coherence for a two-photon state means that the wavevectors of the two photons involved are arbitrary, but the sum (or the difference) between them is well defined. This is the clear consequence of a conservation law. When one photon is converted into two photons in down-conversion momentum needs to be conserved which enforces this well defined sum of the wavevectors. Now in DCQE experiments which-way information and information about the wavevector are complementary. Accordingly you can either perform a measurement on the wavevector of one of the photons involved - then you do not have which-way information, but can predict the wavevector of the corresponding photon on the other side - or you can measure which-way information, but have no information about the wavevector of the detected and the other photon.

So if you choose to measure the wavevector on one side, all the coincidence counts will come from photons on the other side which also have a well defined wavevector and as they go through a double slit you will see the corresponding interference pattern. If you do not single out a narrow wavevector range on the first side than you will also have a superposition of wavevectors on the other side and see an interference pattern with reduced visibility or no interference pattern at all. The choice however does not change the detections on either side. It just allows you to sort out the detection events that form an interference pattern or it makes that impossible. This is independent of the exact time of the choice.

However, what happens is of course still non-local. What you do is - as Scarcelli said - replace the classical electric field with the non-local two-photon probability amplitude. However, this shows pretty clearly that the physics behind the experiment.

 

[San K]

The erroneous statement is this:
Of course polarization affects interference patterns !

What happens, is simply this: when you put the perpendicular polarizers in front of each slit at B, you DO NOT GET AN INTERFERENCE PATTERN.
However, when you put now a polarizer at 45 degrees in front of detector A, and you PICK THE COINCIDENCES of A and B (this removes about half of the photons at B, which do not correspond to a click in A), then it turns out that this SUBSAMPLE shows an interference pattern.
But given that you don't know the polarization of the pair (given that your A-click was after a polarizer at 45 degrees), you will not be able to say through which slit its partner went.
However, if you put the A polarizer to 90 degrees, or to 0 degrees, AND ASK COINCIDENCE AGAIN, you will have a subsample at B that will NOT show interference. This is because knowing the click at A, you know what polarization its partner had, and hence through which slit it went at B.

But in no case, by doing something at A, you see something change at B WHEN ONLY LOOKING AT B.

Vanesch,

Can the above (i.e. subsamples and wavevector) be extended to explain DCQE as well?

http://grad.physics.sunysb.edu/~amarch/

Specifically the fact that the pattern (obtained/filtered/subsampled via coincidence) that is formed on Ds corresponds to what we did to p (eraser or no-eraser) after s was registered at Ds.

 

[San K]

down-conversion momentum needs to be conserved.

this is a bit off topic, i am asking a fundamental question about quantum entanglement:

why does momentum need to be conserved? is it because there is no friction for dissipation of momentum thus the total momentum since the time the two pairs were created needs to remain same?

 

[StevieTNZ]

Well, actually, that would simply be quantum theory. In sum: if you have the potential for which-slit information, there is no interference pattern.

So I think what you are asking is: what is the physical mechanism by which this result occurs? That is presently unknown, even though the quantum description appears complete.

I would question if its potential which-way info that causes the interference to cease.

 

[ejproducts]

I have a related question, I think. I have been reading about the Scully-Druhl experiments where the photons are directed to down-converters, which create a "signal" photon and an "idle" photon, and in which it appears that the idle-photon gives information about which path the signal photon took. This has made me curious about something.

If I have a laser, and fire a photon into a beam-splitter, then my photon can go L or R towards my photo-sensitive paper. If I can detect the path, I understand, I will get no interference pattern, but if I cannot, then I will get an interference pattern as if the photon went along both paths. I place on each path a down-converter, splitting my photon into two lower-energy photons, one - the signal photon - which goes to the photographic paper, and another - the idler photon - which does not. If I place detectors at the ends of the path of the idler photons, I can tell whether my signal photon went L or R. However, I could also direct my idler photons to a single detector, making me unable to see which path my signal photon took. The first scenario would give me no interference pattern, but the second would.

My idler photons travel down a huge length of optical fibre to a human settlement on another planet 10 light years away. At the end of their ten-year journey, they either go into separate detectors, so that I can tell if they went L or R, or into a single detector, so I cannot tell. The decision is made by my friend at the other end, whom I spoke to before conducting the experiment, and the decision is made 9.5 years after my photons hit the down-converters.

I can look at the photographic paper 10 years before it is determined that the idler photons will be able to reveal any information about what path the signal photons took. What will I see?

(Edit: I forgot to put the slits in! Each signal photon would go through a slit, and each idler photon would give information about whether the signal photon went through the L slit, the R slit, or would give no information.)

 

[DrChinese]

Down converted photons do not exhibit interference patterns unless the which path information in its partner is fully erased (as I think you are saying). Generally, it is not possible to erase the information well enough to sense this without coincidence counting. In other words, the pattern you see never changes regardless of what happens on the other planet 10 years later.

BTW: I think if you look at your diagram, the setup on the right is redundant.

 

[ejproducts]

What do you mean by "it is not possible to erase the information well enough to sense this without coincidence counting"?

You are right about the diagram, also. Cheers.

 

[DrChinese]

What do you mean by "it is not possible to erase the information well enough to sense this without coincidence counting"?

You are right about the diagram, also. Cheers.

Suppose you could erase at will. Then you could send signals FTL because Alice could make the interference pattern appear or disappear at Bob's side. But that doesn't happen. Instead, the interference pattern will only appear inside a subset of the events, and the pattern at Bob never varies at all. The subset is one which depends on coincidence counting.

 

[San K]

Suppose you could erase at will. Then you could send signals FTL because Alice could make the interference pattern appear or disappear at Bob's side. But that doesn't happen. Instead, the interference pattern will only appear inside a subset of the events, and the pattern at Bob never varies at all. The subset is one which depends on coincidence counting.

The pattern at Bob never varies at all...and ...it does not vary at Alice either?

i.e. both get a scattering of dots...till subset are created via co-incidence counting

 

[San K]

Suppose you could erase at will. Then you could send signals FTL because Alice could make the interference pattern appear or disappear at Bob's side. But that doesn't happen. Instead, the interference pattern will only appear inside a subset of the events, and the pattern at Bob never varies at all. The subset is one which depends on coincidence counting.

Dr Chinese, if the entire setup was placed in a noiseless environment (i.e. no random photons striking the detector other than the entangled pairs sent/created by the experimenter), would we still need coincidence counting?

 

[marksesl]

The erroneous statement is this:



Of course polarization affects interference patterns !

What happens, is simply this: when you put the perpendicular polarizers in front of each slit at B, you DO NOT GET AN INTERFERENCE PATTERN.
However, when you put now a polarizer at 45 degrees in front of detector A, and you PICK THE COINCIDENCES of A and B (this removes about half of the photons at B, which do not correspond to a click in A), then it turns out that this SUBSAMPLE shows an interference pattern.
But given that you don't know the polarization of the pair (given that your A-click was after a polarizer at 45 degrees), you will not be able to say through which slit its partner went.
However, if you put the A polarizer to 90 degrees, or to 0 degrees, AND ASK COINCIDENCE AGAIN, you will have a subsample at B that will NOT show interference. This is because knowing the click at A, you know what polarization its partner had, and hence through which slit it went at B.

But in no case, by doing something at A, you see something change at B WHEN ONLY LOOKING AT B.

I hate to say this, but I think Vanesch has a misunderstanding of the nature of the coincidence meter. It changes nothing about the general nature of the experiment. If one plots the coincidences between A and B after the fact, and certain correlations show an interference pattern while others correlations do not, it's just that same as if there was no coincidence meter at all and you did the experiment in real time. For example, in delayed erasure any B photon would have still struck before its partner A photon struck, and any state the whole apparatus is in would still produce a visible interference pattern or not (if there was a screen instead of just a detector at B). The coincidence meter is only there to filter out background noise, and if one wanted to alter the experiment at any moment, one could do so and still get valid results just by looing at correlations at some later time without having to wait a long time to get visual conformation in real time.