Can Pinholes Alter Photon Path Deduction in Quantum Mechanics Experiments?

[RandallB]

Continuing the Dopfer discussion from other thread:

If the experimenter reduces the size of the area of radiation of signal and idler photons from the pdc, let's say by use of pinhole(s), then one would see an interference pattern behind the double slit without the use of the coincidence circuit.

Well of course there would be a pattern when you change from a near field experiment (Dopher) to a far field experiment (pinholes) you get different results from an entirely different experiment.

However, in this case, and with the Heisenberg detector at 2f, the two detected triangle pattern intensities behind the Heisenberg lens are broadened wherein both are on top of each other, thus the experimenter cannot deduce path.

The pinhole between the pdc and the double slit acts to reduce the uncertainty in the momentum which increased the uncertainty in position. For there to be signaling from the lens leg to the double slit leg the Heisenberg's uncertainty principle must be revoked -- a violation of quantum mechanics.

There is no “In This Case” as there is no useful purpose for a Heisenberg lens leg with a imaginary double slit image between the pdc and the lens in a far field experiment. You can not expect to destroy the experiment layout and expect to continue to evaluate results based on an double slit image that can no longer exist in a far field set up.

The reason Dopher requires coincidence circuitry and the Heisenberg lens in the first place is to find in the area between the pdf and the lens a double slit image of the real double slit in the other leg. You can only build such a image in a near field approach(no pin holes) – at least IMO.

 

[peter0302]

The reason Dopher requires coincidence circuitry and the Heisenberg lens in the first place is to find in the area between the pdf and the lens a double slit image of the real double slit in the other leg. You can only build such a image in a near field approach(no pin holes) – at least IMO.

What do you think about my idea to place smaller focusing lenses behind the double slit, with the focal point of each lens positioned at each slit, so that the photons emerging are all collimated, and then sending those to a third, larger lens, which focuses all the photons on a single detector? Could it work or would it violate HUP?

 

[RandallB]

What do you think about my idea to place smaller focusing lenses behind the double slit, with the focal point of each lens positioned at each slit, so that the photons emerging are all collimated, and then sending those to a third, larger lens, which focuses all the photons on a single detector? Could it work or would it violate HUP?

This would of course eliminate the possibility of producing a pattern even if there PDC were in a Far field configuration with the double slits. It is the geometry of the H-lens and the correlations that can allow a pattern to be built behind the real slits but with only one detector accumulating all the photons there is no useful geometry available to reconstruct a double slit image in the other path so none of the patterns will be able to be produced; not at F1, F2, or the pattern at the real double slit.

The PDC itself is acting like a out of focus lens with a wide f-stop (far field), it is the H-lens and the correlations with an unobstructed pattern behind the real double slit that eliminates walk-off effect photons from the PDC allowing only counts that in a sense artificially stop down the “PDC lens” to a very small aperture. Much like a camera, if you can get by with an f-stop of 32 you don’t need to worry about focusing the lens much. But with a wide open F-stop an out of focus lens (a near field PDC) won’t give a useful image.

 

[peter0302]

but with only one detector accumulating all the photons there is no useful geometry available to reconstruct a double slit image in the other path so none of the patterns will be able to be produced; not at F1, F2, or the pattern at the real double slit.

Look at the picture attached, which is Figure 4.5 from the Dopfer thesis.

D1 is fixed at the focal point of the Heisenberg lens (it does not scan its x-axis). D2 does scan the x-axis and a pattern emerges when the D1 and D2 photons are coincided.

If we could ensure that every signal photon coming out of the crystal actually hit the detector D1, would that not eliminate the need for coincidence counting?

 

[RandallB]

If we could ensure that every signal photon coming out of the crystal actually hit the detector D1, would that not eliminate the need for coincidence counting?

Moving over to the image slit side does not improve potential results.
It is not that forcing D1 to collect all photons that would have entered the H-Lens will “eliminate the need for coincidence counting” the problem is it will eliminate the ability to do coincidence counting . With no ability to selectively measure photons coming through the real double slit there is no meaningful coincidence counting at D2.

Dopher confirmed that the only way to see a pattern by moving D2 is with coincidence counting with a stationary D1 that cannot exist in your new set up.

A simple classical analysis of the size of the PDC source relative to the distance to and size of the physical double slit puts that configuration well within the out of focus near field range. This is the main difference Dopher & the Backwards C set ups. Cramer can confirm avoiding the walk off issue by setting up in the far field (instead of the near field as Dopher uses) will give a pattern is the easy part for him. His technical issues with the rest of his experiment are not directly related to the near field issues shown here in Dopher.

I consider Dopher an inverse of a typical DSQE where a pattern is erased by correlations; as she builds a pattern where there was none by using correlations. IMO she deserved to have had a paper published under her name summarizing her thesis which was probable to long for a peer review publication. I assume she at least received a good grade on her thesis work.

 

[peter0302]

But you're overlooking the fact that the only reason the coincidence counting is necessary is to make sure we only plot photons at D2 which correspond to photons detected at D1. The pattern that emerges at D2 is just a plot of ALL the photons that emerge from the real slit which coincide with photons that were detected at D1. The photons at D2 could have been detected in any order so long as the only ones we look at were ones that hit D1. Therefore, if ALL the photons hit D1, we could look at all the photons hitting D2 and see a pattern.

 

[RandallB]

Therefore, if ALL the photons hit D1, we could look at all the photons hitting D2 and see a pattern.

Well yah, that is the point - it means any photon hitting D2 will be counted with or without cooralation with your new D1 hits. because you count all the photons in the d1 path. It will of couse be a much much higher number of counts than when you limit D1 to counting only those in that hit one spot.

The trick Dopher figred out was that by counting fewer D2 photons would build a pattern by picking select photons at D2 (not all) based on coincidence counting with a fixed D1 in the H-lens set up. The purpose of coincidence counting is not just to be sure you pick photons that split in the PDC which is all your set up can do.

 

[peter0302]

Well yah, that is the point - it means any photon hitting D2 will be counted with or without cooralation with your new D1 hits. because you count all the photons in the d1 path. It will of couse be a much much higher number of counts than when you limit D1 to counting only those in that hit one spot.

So you agree with me that the coincidence counter wouldn't be necessary here?

 

[RandallB]

So you agree with me that the coincidence counter wouldn't be necessary here?

What do you mean by "here".
What new thing, that Dopher was not looking at, are you intending to measure?
And what do you think you will see?

 

[peter0302]

Take Figure 4.5 up there.

Assume EVERY signal photon (top half) hits D1. Ignore everything else that happens inbetween the crystal and D1. (Ignore whether this is possible for the moment).

Replace D2 with a white screen.

I expect to see interference fringes at D2.

You disagree?

 

[RandallB]

I expect to see interference fringes at D2.

You disagree?

It is necessary to use coincidence counting without it reducing the photon count at D2 to the correct few that can produce a interferance pattern is the only way to get that pattern.
Forcing D1 to read all photons and not allow D2 to reduce its count down to the correct few is the same as not counting and getting no pattern. Reread #5.

 

[peter0302]

You're assuming a priori that what happens to a particular photon at D1 has no effect on what happens to its twin at D1. But I believe the Dopfer experiment confirms that this is - at least - an unproven assumption. But that is the very assumption that Cramer, et al are trying to prove. What is the basis for that assumption other than causality postulates and the so-called no-signalling theorems?

 

[RandallB]

You're assuming a priori that what happens to a particular photon at D1 has no effect on what happens to its twin at D1.

You mean it’s Twin at D2
You need to take some time to think about what your reading and writing.
I didn’t make that assumption here you did.
You built the case that if 100% of the photons at D1 were destructively destroyed in detection in order to make correlation counts with the photons at D2 you would see an interference pattern. And based on your assumption (that what happens to photon at D1 has no effect on its twin at D2) you “eliminate the need for coincidence counting” because if you change what happens to the photons at D1 by removing D1 so they are not destroyed and there is no possibility of coincidence counting you expect you will still see an interference pattern.

You simple have your facts wrong!
No theory expects, or observed results have shown that D2 sees an interference pattern at D2 without using coincidence counting to selectively observe only a much smaller number of photons than are passing through that double slit.
I’m not a priori assuming anything – I’m going by the observed facts reported in Dopher; and they match the no coincidence counting expectations of both Classical Wave and OQM calculations. The two theories have never disagreed on this point.
If Dopher had shown differently it would have meant something was wrong with OQM and her results did not show or claim that.

But I believe the Dopfer experiment confirms that this is - at least - an unproven assumption. But that is the very assumption that Cramer, et al are trying to prove.

Nonsense; if you believed that – than why are you so adamantly opposed to Cramer doing his experiments? It defies logic. Other than you like your interpretation of how “Weird Actions at a Distance” happens, your preference whatever it is comes with no facts to support it.

Also, for the record Cramer has made clear in his lectures he is not “trying to prove” Backwards Causality” he is experimentally trying to test it to the point of verification or falsification and has stated that the odds of verification are small.[/QUOTE]What is the basis for that assumption other than causality postulates and the so-called no-signalling theorems? [/QUOTE] So on this point I don’t know – it is your assumption - what is your basis?

 

[peter0302]

No, Randall, you're not addressing my arguments. If my occasional typo is the problem then I apologize but I don't think that's it. We're talking past each other.

I am making the following hypothesis:

If 100% of the signal photons exiting the crystal are path-destroyed by forcing them (through a lens or otherwise) to all be detected at D1, then 100% of the the idler photons coming out of the same crystal will behave as though they are not entangled, i.e., like a normal laser would, and show a visible interference pattern.

I hypothesize that the only reason coincidence counting is necessary in Dopfer's set up is because at any given time only a fraction of signal photons emerging from the crystal are actually hitting D1 and thereby having which-path destroyed. Therefore, obviously coincidence counting is necessary to select the subset of idler photons that correspond to those few signal photons where which-path was destroyed.

But, if 100% of the signal photons are which-path destroyed, I do not see why we would need to throw out ANY of the idler photons in order to make our pattern, and thus why we would need coincidence counting The idler photons should behave like normal, non-entangled photons. By the way, when Zelinger explains Dopfer, he says that the reason entangled photons ordinarily don't create an interference pattern is because it remains, in principle, possible to detect which-path in the entangled twin, and thereby that would violate the HUP. However, by destroying which-path in the entangled twin, you WILL see an interference pattern in the photons which you know (thanks to the coincidence counting) correspond to those where which-path was destroyed. Every DCQE experiment confirms this. But - if you can destroy which path for all of them, why would there be a need to select a subset?

I think it's a very simple logical step to then conclude that if you could destroy which-path for 100% of the signal photons, you would see interference in 100% of the idlers without the need for coincidence counting.

If I'm right, the HUP is not violated because you never observe which-path AND interference for the same photon. In fact, no one has yet pointed out an accepted principle of QM that this idea violates, other than so-called non-signaling theorems which themselves assume, a priori, that what happens to one photon cannot effect what happens to the other.

Nonsense; if you believed that – than why are you so adamantly opposed to Cramer doing his experiments? It defies logic. Other than you like your interpretation of how “Weird Actions at a Distance” happens, your preference whatever it is comes with no facts to support it.

I deserve a little more credit than that, Randall. I don't have a preference or a belief. I have no idea whether what I'm proposing will work or is even possible. In fact, I've said many times I do not expect it IS possible to destroy which-path for 100% of the signal photons coming out of the crystal - because of the HUP! But in any event I don't think it's obvious and therefore it is worth testing.

I am (I would not say adamantly) opposed to Cramer's experiment as it stands now because he has yet to prove that he can even do what I'm proposing, which is less of a feat than what he's proposing. If he can't even make a visible interference pattern out of entangled photons - irrespective of the chronology of the experiment - it doesn't matter how sensitive his CCD is or how many km of fiber optics he has. Clearly he should try my far cheaper proposal first.

And based on your assumption (that what happens to photon at D1 has no effect on its twin at D2)

It is possible that I misspoke along the way, but my hypothesis is the opposite. My hypothesis (and Cramer's, and Zelinger's) is that if you have two entangled photons, and you detect one in such a way that it is impossible to surmise position/path, then the other will remain in superposition, and, if sent through a double slit, will exhibit interference.

From that, I surmise that if you have two beams of photons that are position/momentum entangled, and you manage to detect one beam in such a way as to destroy the possibility of learning which-path for 100% of the photons, the other beam will behave like an unentangled beam and display visible interference, also remaining in superposition.

Using this method, if my hypothesis is right, one would be able to send a signal with the idler photons by altering the method of detection of the signal photons.

PLEASE tell me if you see a flaw in that logic or what principle of QM disproves my hypothesis. All I'm asking for is an experiment or accepted principle that disproves what I'm proposing but so far no one has provided one.

 

[RandallB]

No, Randall, you're not addressing my arguments.
I am making the following hypothesis:

If 100% of the signal photons exiting the crystal are path-destroyed by forcing them (through a lens or otherwise) to all be detected at D1, then 100% of the idler photons coming out of the same crystal will behave as though they are not entangled, i.e., like a normal laser would, and show a visible interference pattern.

Yes I did - back in post 5 – doesn’t matter if it is a single beam of light is alone or has some “entangled” duplicate beam going unused elsewhere. If the source is in the size and shape of the PDC used in Dopher a interference pattern cannot be created period . Your argument / hypothesis died there.

If you do not understand what near field & out of focus means you cannot just ignore it so you can press on like a bull in a china shop with the same unfounded argument and flawed logic.

As I already said using only the idler path alone using a source the size and shape of this PDC, by only using the idler path (no correlation counts) it does not matter if the source produces entangled photons or not, neither Classical Wave or QM predictions care because both predict the same no interference pattern due to the near field out of focus configuration.
And it is clear to me the Dopher results confirm this rather obvious conclusion made by both theories. Where the two theories part ways is in explaining how a pattern is extracted in an inverse DCQE manner by using correlation counting. The Classical or at least a LR-Local version of Classical has not been able to do so, while QM and Non-Locals can. (I'd allow BM as a Non-Local Version Classical)

 

[peter0302]

I understand the distinction perfectly (I certainly understand photography) and I thought it was obvious that we would be using an in-focus configuration and Type II beamlike SPDC. Now what's your response?

 

[RandallB]

I understand the distinction perfectly (I certainly understand photography) and I thought it was obvious that we would be using an in-focus configuration and Type II beamlike SPDC. Now what's your response?

Of course it is not obvious you desired to set up a far field experiment – you had stated you were modifying a Dopher configuration. Type I or Type II doesn’t matter, the Dopher experiment is clearly a Near Field configuration wrt it both the real double slit and the double slit image in the other leg.

If while setting up and calibrating the D2 measurement range in the diffusion pattern behind the double slit an experimentalist instead saw a interference pattern you would certainly expect to still see an interference pattern by reducing the count photons used with a random number generator selecting only 1 in a thousand photons. If a random number generator could have produced an interference pattern it would have been grossly irresponsible to report correlation counts producing interference patterns as something special, without disclosing that a random number generator could do the same thing.

Even though I do not read German (And it is still beyond me why such a well done documentation and important experiment has not been translated into English) it is clear to me she saw a dispersion pattern not an interference pattern during the set up.

 

[peter0302]

And it is still beyond me why such a well done documentation and important experiment has not been translated into English

At least we agree on something ;)

it is clear to me she saw a dispersion pattern not an interference pattern during the set up.

No, she saw an interference pattern at D2 when D1 was at the focal point of the Heisenberg lens, and she saw a dispersion pattern at D2 when D1 was far from the focal point. The interference pattern would have been visible to the naked eye if 100% of the signal photons had reached D1. (Which I don't thnk is possible).

Also I forgot that she used a lens at D2 which - I can only assume - replicates a far field condition just like DCQE did.

The reason to use beamlike type 2 is to narrow the beam sufficiently so that you can hope to collect all the photons at D1.

Well, sorry but no more point in arguing, I think I've said all I can. Hopefully I'll be able to scrap together the components and test this myself in the next few months.

 

[Cthugha]

I do not know, whether this hits the central point of the discussion, but let me comment on this topic by translating or at least summing up a few passages of the thesis as good as I can:

I am making the following hypothesis:

If 100% of the signal photons exiting the crystal are path-destroyed by forcing them (through a lens or otherwise) to all be detected at D1, then 100% of the the idler photons coming out of the same crystal will behave as though they are not entangled, i.e., like a normal laser would, and show a visible interference pattern.

I hypothesize that the only reason coincidence counting is necessary in Dopfer's set up is because at any given time only a fraction of signal photons emerging from the crystal are actually hitting D1 and thereby having which-path destroyed. Therefore, obviously coincidence counting is necessary to select the subset of idler photons that correspond to those few signal photons where which-path was destroyed.

The topic of having interferences at D2 without coincidence counting is discussed in the Dopfer thesis on page 45. There it is stated, that the single photons have coherence properties, which are comparable to thermal light. Their phases are uncorrelated (just the phase for the two photon state is well defined) and will therefore usually not produce an interference pattern. However, one can increase spatial coherence by using a smaller part of the source, which means increasing the distance between the source and the double slit. On page 45 Dopfer states, that the minimal distance to have an interference pattern occur without doing coincidence counting is 770mm.

Dopfer then develops a criterium to have an interference pattern occur in the coincidence counts. She argues, that you need enough "allowed directions" for the photon pairs in order to be able to see an interference pattern. She then states, that one can only see the part of the intensity pattern, for which the needed momentums can be realized. (Sorry for the strange usage of language. The terminology in the original thesis is also a bit sloppy here.)

As an analogy she thinks of D2 as a source of photons and the nonlinear crystal as a mirror. The photons go through the double slit and are reflected towards the detector D1. Only if the distance between the crystal/mirror and the double slit is small enough, a picture of the double slit will arrive at the detector, because otherwise the mirror will be so small, that only a small part of the interference pattern will be reflected and one will not be able to see interferences anymore. She then states, that the maximum distance for interferences to occur in coincidence counting is 106mm.

She then concludes that single photon counting interferences and coincidence counting interferences are complementary in principle, so it is impossible to see both at once with full contrast. She quotes an article here (D.M. Greenberger, M.A. Horne, A. Zeilinger, Multiparticle Interferometry and the Superposition Principle,
Physics Today, 22-29 (August 1993)) and says, that it holds more information about this complementarity, but I did not check that.

 

[peter0302]

Thanks Cthugha! I think it hits on Randall's point head on though not so much on mine. My point is let's use something coherent and beamlike, such as Cramer's set up (he uses beamlike type 2 SPDC) and in focus (either by using far field or a lens). Now shouldn't we expect to see a visible interference pattern at D2 when we cause all the signal photons to be detected at D1?

I would note that my idea is not entirely unlike Cramer's, but I eliminate the need for miles of fiber optics, for one thing, and a hyper-sensitive CCD.

 

[RandallB]

I do not know, whether this hits the central point of the discussion, but let me comment on this topic by translating or at least summing up a few passages of the thesis as good as I can:
...
As an analogy she thinks of D2 as a source of photons and the nonlinear crystal as a mirror. The photons go through the double slit and are reflected towards the detector D1. Only if the distance between the crystal/mirror and the double slit is small enough, a picture of the double slit will arrive at the detector, because otherwise the mirror will be so small, that only a small part of the interference pattern will be reflected and one will not be able to see interferences anymore.

She then states, that the maximum distance for interferences to occur in coincidence counting is 106mm. .

Thanks so much.
Selective Google translations for German can be hard to sort out.
I disagree with her “Mirror” analogy – I look at it as correlations allow the PDC to act as a Pinhole Camera using D2 as a faux source when the PDC is otherwise much to large to serve as a “Pinhole”.

Taking a closer look at the German text around the 106mm statement – do you think it fair to say it means to produce a random dispersion pattern from a single PDC beam that only coincidence counting with the other PDC beam could recover an interference pattern the distance to the double slit needs to be less than 106mm?

And the range between 106mm to 707mm is kind of a fuzzy area between a clear Near-field verses Far-field condition.

Thus with her experiment using a distance of 702.2 nm from the PDC to the ‘Doppelsplat’ it is well inside the near-field range. (Even deeper than I’d thought.)

 

[Cthugha]

Thanks so much.
Selective Google translations for German can be hard to sort out.

Oh, I know. Some spam mails one gets in Germany are just English ones, which have been translated word by word by using google. The result are very funny mails.

I disagree with her “Mirror” analogy – I look at it as correlations allow the PDC to act as a Pinhole Camera using D2 as a faux source when the PDC is otherwise much to large to serve as a “Pinhole”.

She calls her mirror analogy the Klyshko picture. I just know, that he was one of the pioneers in down conversion, but I do not know, whether this picture is just a very simplified toy model or claims to be realistic.

Taking a closer look at the German text around the 106mm statement – do you think it fair to say it means to produce a random dispersion pattern from a single PDC beam that only coincidence counting with the other PDC beam could recover an interference pattern the distance to the double slit needs to be less than 106mm?

And the range between 106mm to 707mm is kind of a fuzzy area between a clear Near-field verses Far-field condition.

If I get you right, I think this is indeed what the text says.

Thus with her experiment using a distance of 702.2 nm from the PDC to the ‘Doppelsplat’ it is well inside the near-field range. (Even deeper than I’d thought.)

I think the picture she used to describe her setup is a bit misleading. The 702.2 nm are the wavelength of the photons she used. The distance from the PDC to the double slit is 40mm as Dopfer states on page 45.

 

[peter0302]

Randall, let me ask you this, and stop me at any point you disagree. (Anyone else please feel free to chime in as well).

If a general double-slit experiment were set up with far field, you would expect an interference pattern from photons going through the double slit ordinarily.

However, if the photons were entangled with others that went off into space, we would not expect such a pattern or else it would be possible - in principle - to derive which-path info from the entangled twins, and defeat complimentarity.

In such a situation, though, if we could detect the entangled photons in such a way as to eliminate any possibility of detecting which-path info via the entangled twins, we would expect the visible interference pattern to re-emerge.

Correct or not?

 

[RandallB]

I think the picture she used to describe her setup is a bit misleading. The 702.2 nm are the wavelength of the photons she used. The distance from the PDC to the double slit is 40mm as Dopfer states on page 45.

Thanks that is a good bit more realistic (the nm range just didn’t make sense).
It’s been a year since I tried to decipher the German an I think I had somehow guessed about 40 mm at the time. But I’d never drew out the detail she had given on a maximum of 106mm from the PDC to be sure the test is within the near-field. 40 mm is about what I’d expect for getting an experiment deep inside the near-field range 106 mm where the far-field doesn’t become clear until 707 mm away from the PDC. Still a lot of meticulous detailed work to extract the observations she documented.

Thanks again – important information to me, I’ll need add to my old notes on Dopfer.
That is when I find the right thumb drive that has that file – sometime keeping track of an old file is as hard as finding a notation on a scrap of paper.

 

[Cthugha]

In such a situation, though, if we could detect the entangled photons in such a way as to eliminate any possibility of detecting which-path info via the entangled twins, we would expect the visible interference pattern to re-emerge.

No, I don't think so. Have a look at the part near the end of the Dopfer thesis, where she tests some small changes to the setup. For example she puts a beamsplitter between the Heisenberg lens and the detector D1, puts D1 at both exits of the beamsplitter at equal distance to the lens at before and does coincidence counting in both positions. You can see the result in picture 4.42 at the end of page 95. You see, that both coincidence count experiments lead to an interference pattern, but they are shifted by pi due to the difference between reflection and transmission. The sum of both now gives an usual superposition of two single slit diffraction patterns - just what you see directly at D2. In this setup, it is clear, that you won't see an interference pattern in the detections of D2 alone, even if you have ideal beam splitters and ideal detectors, which destroy any which-path information, so I do not think, it is possible to have an interference pattern appear at one detector only.

 

[RandallB]

Randall, let me ask you this, and stop me at any point you disagree. (Anyone else please feel free to chime in as well).

If a general double-slit experiment were set up with far field, you would expect an interference pattern from photons going through the double slit ordinarily.

However, if the photons were entangled with others that went off into space, we would not expect such a pattern or else it would be possible - in principle - to derive which-path info from the entangled twins, and defeat complimentarity.

IMO incorrect at this point.
But an issue debated in other threads in this forum and I’ve never seen any observed evidence that settles the issue documented in something per reviewed.

For me, I satisfied by the preliminary work by Cramer (in trying to set up his RC test) confirms that a single beam from entanglement when viewed in the far-field still produces a interference pattern not a dispersion pattern. That is not a detail holding up his RC experiment, his problems are much larger than that.
BUT that is just my opinion Cramer has not published or even lectured on this fine point AFAIK.

As to defeating complimentarity – before that can be done you need a clear definition of just what that is.
NOW THERE is a challenge for you; just try to find a clear and concise statement or develop one yourself as to exactly what complimentarity is and means! With just a bit of research you’ll need to open a new thread on that one.

 

[peter0302]

You can see the result in picture 4.42 at the end of page 95. You see, that both coincidence count experiments lead to an interference pattern, but they are shifted by pi due to the difference between reflection and transmission. The sum of both now gives an usual superposition of two single slit diffraction patterns - just what you see directly at D2. In this setup, it is clear, that you won't see an interference pattern in the detections of D2 alone, even if you have ideal beam splitters and ideal detectors, which destroy any which-path information, so I do not think, it is possible to have an interference pattern appear at one detector only.

That makes perfect sense because that alternate set up is basically a Kim DCQE - the erase/non-erase decision is made by the 50/50 splitter, which does introduce a phase element.

But earlier in her experiment, the erase/non-erase decision is made just by moving the detector out of the focal point. And that's why the interference pattern in Figure 4.18 is symmetric. So there should be no phase element between the erase/non-erase scenario in that situation.

IMO incorrect at this point.
But an issue debated in other threads in this forum and I’ve never seen any observed evidence that settles the issue documented in something per reviewed.

I agree with you there. This is a claim made by Zelinger and it is the way that I have been interpreting Dopfer, but I agree this is something that needs to be established experimentally first before we can make any further progress in this topic.

For me, I satisfied by the preliminary work by Cramer (in trying to set up his RC test) confirms that a single beam from entanglement when viewed in the far-field still produces a interference pattern not a dispersion pattern. That is not a detail holding up his RC experiment, his problems are much larger than that.

If you're right, and Zelinger's wrong, then Cramer still has one more thing to show before we should pay any more attention to him: can he cause the pattern in one beam to change by doing something to the other beam? I don't care what it is, and I don't care whether it's retro-causal. He needs to take that step first, and I don't think he can do it.

The very first time I read Cramer's paper I thought "there will always be an interference pattern no matter what." It sounds like that's what you think too. After reading Zelinger's comments about Dopfer, and then Dopfer itself (at least attempting to), I concluded the opposite - that there would always be a dispersion pattern unless great care was taken to handle not just some, but ALL of the photons in such a way as to erase position info. I do not believe Cramer's simple combining of fiber optic beams is sufficient, and I think all this talk of a CCD is a red herring.

Lastly, the more I think about it, the more I think that the far field / near field issue is also not the problem. It certainly explains why there's a lens behind the slits in Figures 4.5 and 4.6, but I think that's it. In any event, I still want to test what would happen if we used beamlike SPDC in a far field setup and forced (through lenses or whatnot) all the signal photons to strike D1 simultaneously. Would we see an interference pattern or a dispersion pattern at D2?

On a side note, does anyone know how a beamlike SPDC-type2 setup would cost?

 

[Cthugha]

That makes perfect sense because that alternate set up is basically a Kim DCQE - the erase/non-erase decision is made by the 50/50 splitter, which does introduce a phase element.

But earlier in her experiment, the erase/non-erase decision is made just by moving the detector out of the focal point. And that's why the interference pattern in Figure 4.18 is symmetric. So there should be no phase element between the erase/non-erase scenario in that situation.

This is not the point here. The decision is not between erase and non-erase, but between erase usually and erase and apply an additional phase shift of pi. This part of the experiment is not a DCQE as the lens is positioned before the bs and the detector is placed at focal distance in both positions. You would get the same phase shift of pi by just using a mirror instead of a bs. This means, that if there was an interference pattern at D2 alone, you could shift it around "at a distance" by just having two detectors D1 at focus distance to the Heisenberg lens and inserting or taking out a mirror. That does not sound realistic.

Also the fact that the interference pattern looks symmetric does not mean much. If you have a look at the standard paper about delayed choice quantum erasers (this one:http://arxiv.org/abs/quant-ph/9903047), you will notice, that there are two interference patterns at two detectors, shifted by pi. Both are symmetric, but one has a sine shape and the other has a cosine shape.

Another point showing the problem without using any external phase shifts can be seen on page 65 of the Dopfer thesis. Here she just puts D2 at a fixed position behind the middle of the double slit and moves D1 through the focal plane - and sees an interference pattern in the coincidence counts as well. Now guess, what you will get, if you mark an interference minimum for the position of D1 when D2 is fixed and an interference minimum for the position of D2 when D1 is fixed and afterwards put both detectors to these minima positions.

 

[peter0302]

This is not the point here. The decision is not between erase and non-erase, but between erase usually and erase and apply an additional phase shift of pi.

I don't think that's right. If we're talking about the same picture - Fig. 4.39, the transmit beam hits a detector positioned at "f" - which is the focal point, i.e., the erase case, whereas the reflect beam hits a detector positioned at "2f" - which is the non-erase "image" plane. Are you talking about a different picture?

This part of the experiment is not a DCQE as the lens is positioned before the bs and the detector is placed at focal distance in both positions.

Ok I think we are talking about a different picture. Where are you in the paper?

You would get the same phase shift of pi by just using a mirror instead of a bs. This means, that if there was an interference pattern at D2 alone, you could shift it around "at a distance" by just having two detectors D1 at focus distance to the Heisenberg lens and inserting or taking out a mirror. That does not sound realistic.

You don't get a phase shift in moving the detector D1 from f to 2f. No mirrors or beamsplitters. Focus on Figs. 4.5-4.6.

Also the fact that the interference pattern looks symmetric does not mean much. If you have a look at the standard paper about delayed choice quantum erasers (this one:http://arxiv.org/abs/quant-ph/9903047), you will notice, that there are two interference patterns at two detectors, shifted by pi. Both are symmetric, but one has a sine shape and the other has a cosine shape.

They are certainly not symmetric. Look at the difference between Figure 4.18, for example, in Dopfer, and Figs. 3 or 4 in Kim.

Another point showing the problem without using any external phase shifts can be seen on page 65 of the Dopfer thesis. Here she just puts D2 at a fixed position behind the middle of the double slit and moves D1 through the focal plane - and sees an interference pattern in the coincidence counts as well. Now guess, what you will get, if you mark an interference minimum for the position of D1 when D2 is fixed and an interference minimum for the position of D2 when D1 is fixed and afterwards put both detectors to these minima positions.

I'm not following you here. This configuration - keeping D2 fixed and making an image from D1 - is simply a reversal of the configuration I'm focusing on. All this shows is that you see two clean spikes when D1 is positioned to correspond to the slits, and a nice interference pattern when D1 is positioned at the focal point.

 

[Cthugha]

I don't think that's right. If we're talking about the same picture - Fig. 4.39, the transmit beam hits a detector positioned at "f" - which is the focal point, i.e., the erase case, whereas the reflect beam hits a detector positioned at "2f" - which is the non-erase "image" plane. Are you talking about a different picture?

Now it gets a bit complicated as she did not show individual pictures for all the small variations she tried. After picture 4.39, which shows a DCQE setup she mentions how moving all the detectors around changes (or does not change) the results. At first she moves the detector at 2f around (upper picture of 4.40), then she destroys which-way information by using a larger detector at 2f in picture 4.41 (which does not recreate the interference pattern of course). Now the picture I talk about is 4.42, which is just the symmetric version, in which the detector at f and 2f just change the exit port of the beam splitter. As you see in the lower panel of picture 4.42, both positions produce interference patterns in the coincidence counts of D2 and the detector at f, but with a phase shift of pi. So now you could easily also put one detector at focus distance at each of the exit ports, take the beam splitter out and instead put a mirror at its place and take it out again. Just by putting the mirror in (or taking it out), you will be able to shift the interference pattern by pi.

You don't get a phase shift in moving the detector D1 from f to 2f. No mirrors or beamsplitters. Focus on Figs. 4.5-4.6.

Yes, of course not. See above, what I meant beforehand.

They are certainly not symmetric. Look at the difference between Figure 4.18, for example, in Dopfer, and Figs. 3 or 4 in Kim.

Really? To me the peak positions (not the peak height of course) seem to be distributed symmetrically around the central peak/dip.

I'm not following you here. This configuration - keeping D2 fixed and making an image from D1 - is simply a reversal of the configuration I'm focusing on. All this shows is that you see two clean spikes when D1 is positioned to correspond to the slits, and a nice interference pattern when D1 is positioned at the focal point.

Ehm, now I can't follow you. Look at the upper panel of figure 4.23. Here D2 is fixed and D1 is moved while it stays inside the focal plane of the Heisenberg lens. This is not just two spikes, but a whole interference pattern. This assures, that there is not just one focal point, but a focal "line". So your ideal detector, which is intended to detect every photon will also need to be at least as large as the width of this interference pattern is to get every photon count. Now my claim is: Move D1 to one of the points on this line, where you will have a minimum in the correlation counts and fix it there. Now move D2 back and forth just like before. I bet, you will get an interference pattern, where minima and maxima exactly change place compared to the case, when D1 is located exactly at the center. Thus an ideal photon counter, which detects every photon, will give you two interference patterns at D2, which add up to the usual superposition of two single slit diffraction patterns.

Of course this "spreading" after the Heisenberg lens will only happen for a source, which is not a point source, but has some finite volume. On the other hand, sources, which are very small, will already show a lot of diffraction directly. This will destroy any entanglement right at the beginning. Somewhere in the thesis, Dopfer gives a lower bound for the needed size of the source, but I am too lazy to look it up now. It's already 2 am. ;)