# Delayed Choice Bell-state Quantum Eraser

1. May 28, 2006

### Burnsys

http://www.joot.com/dave/writings/articles/entanglement/spookiness.shtml

http://www.joot.com/dave/writings/articles/entanglement/quantum-eraser.png

1. a laser fires photons into a Beta Barium Borate (BBO) crystal;
2. the crystal entangles some of the photons; and then
3. entangled photons travel to two different detectors: A and B.

Placed between the crystal and detector B is a double-slit, like in the previous experiments. Immediately in front of detector A is a polarizing filter that can be rotated.

Each slit is covered by a substance that changes the polarization of a photon. Consequently, the left-hand slit will receive photons with a counter-clockwise polarization, and the right-hand slit will pass photons with a clockwise polarization.
-----------------------------------
If we measure polarization at detector A then we have wich-way information and the interference pattern disapear at B, if not we have interference pattern at detector B

Now suppose we place a 1 millon km long fiber optic between the BBO crystal and detector A so that each photon will arrive 3 seconds later at detector A.

Now we have 3 seconds to decide if we want to get WichWay information or not after the photons hited detector B.

So, if i see an interference pattern at B then i set detector A to measure Polarization while the photons are still traveling.. What would be the results of this experiments?

Last edited: May 28, 2006
2. May 29, 2006

### vanesch

Staff Emeritus
This comes back and back and back. You will not see an interference pattern at B. You only find an interference pattern at B *IN COINCIDENCE* with A. The "interference pattern" is in fact a "correlation pattern": if you look at all clicks at B WHICH CORRESPONDED TO A CLICK IN A, then the hits at B show an interference pattern. If you look at all the hits at B, irrespective of what might happen at B, then you'll see nothing.

This is the usual misunderstanding of these experiments, but I can understand why: very often the publications "over-sell" the result, and make it sound AS IF there was a bare interference pattern at B only, which then triggers (rightly) all these questions about paradoxes or FTL communication.

3. May 29, 2006

### Burnsys

Then detector B is not a screen and i will not see somenthing like this :

http://www.physics.utoledo.edu/~ljc/interfer03.jpg

???

Just trying to understand. Thanks

4. May 29, 2006

### vanesch

Staff Emeritus
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.

5. Nov 14, 2010

### Kyle-DFW

Vanesch:

I agree with your "subsample" comments. Since you've earned credit in my book as someone who is well-versed on the details, I'm wondering if you have a theory or explanation for why an interference pattern is observed in the simple double-slit experiment where regular (non-entangled) photons are used and the photons are shot at the slits one at a time?

It seems to me that one must conclude that individual photons are interfering with themselves, and therefore an individual photon must truly be a wave which is passing through both slits simultaneously. Therefore, the particle-like properties of a photon (like position) may not actually be present until the moment of observation where the wave of potential locations collapses to a single measured location. The possible measured locations are then constrained to the interference pattern.

I suppose another possibility is that our belief that we can emit individual photons may be wrong.

6. Nov 15, 2010

### DrChinese

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.

7. Nov 22, 2010

### Kyle-DFW

When I first read this thread, I tended to agree with the comments from vanesch that the interference pattern was an artifact of looking only at a subsample of photons which are detected at B after a corresponding photon is detected at A.

This would seem to make the experiment not seem so mysterious because it would suggest that only photons that come through the slits with opposite polarizations will generate an interference pattern.

However, after studying again the information I have been able to find about these experiments online, I realize vanesch made a key mistake:

He stated that the interference pattern is seen when you look at the subsample of photons at B that correspond to a click in A. IT IS THE OPPOSITE. When the path information is available at A (coincidence clicks), the which-path information is available and there is NO INTERFERENCE at B. You get two bands as you would expect if photons were classical particles. When there is no which-path information available, THIS IS WHEN YOU GET AN INTERFERENCE PATTERN. Since on each measurement, there is only a single photon fired at the slits, the presence of an interference pattern forces one to conclude that a SINGLE PHOTON at that point is in fact a wave traveling through both slits simultaneously and interfering with itself. When the photon is finally detected at B, it again looks like a particle because it is seen at a discrete location in space, but the location where it is found will never be outside of the bounds of the interference pattern.

From what I have read, it also seems reasonable to say that polarization really does NOT have an effect on the interference pattern because only coherent (in-phase) photons are required to get an interference pattern. Polarization is not required to see it, and in the experiment, the polarized photons are coherent. In other words, coherent non-polarized photons can generate an interference pattern in the absence of which-path information, but so can coherent polarized photons.

References:

http://davidjarvis.ca/entanglement/

http://en.wikipedia.org/wiki/Coherence_(physics [Broken])

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8. Nov 23, 2010

### Joseph14

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9. Nov 23, 2010

### Joseph14

To summarize the results:
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

My interpretation
1. The photons are coherent so you get interference (even without coincidence counting)
2. QWP put the photons out of phase (by a quarter wave) so now there is no interference because the QWP messed up the coherence
3. Polarizer at A now selects out the photon polarizations such that the fast axis and slow axis of the quarter wave plate don't mess up the interference

10. Nov 23, 2010

### Joseph14

It isn't the opposite look at the experiment again. The results are always based on coincidence counts.

The spacing is close enough that you wouldn't get two bands, they would blur together.

The polarization does have an effect for the case when QWP are in place because the coherency is destroyed based on the polarization of the photon.

11. Nov 23, 2010

### Kyle-DFW

I've been re-reading and giving a lot of thought to this document:

My current belief (for today anyway lol) is that we are really not even dealing with an issue of subsamples here.

If I understand correctly, when a polarizer is present at detector A (detector p in the document), meaning which-path information is available, the position of all photons encountered at detector B (detector s in the document) is still recorded.

Because the entangled photons come through one at a time (because the BBO crystal rarely splits a photon) the computer counter knows that the photon at A should arrive with virtually no time difference to the arrival at B. If the photon at B is recorded and there is a coincident photon recorded at A (with the polarizer in place), you could say that the photon at B came through slit 1 for example. If the photon is recorded at B and within a very short time window, there is no coincident photon recorded at A (because it was blocked by the polarizer), then you would know that the photon at B came through slit 2.

When the experiment is configured this way, the positions for ALL photons encountered at B are still recorded, and there is NO interference pattern. You get two bands, which is what you would expect if each photon passed through only one slit or the other as a classical particle.

Now as I understand it, you can restore the interference pattern without changing ANYTHING about the detector B setup or the photons entering it. All you have to do is "erase" the which-path information at detector A by either removing the polarizer (whereby the photon will be absorbed at detector A with all chance to measure its polarization lost) or by rotating the polarizer at A to 45 degrees where it would be impossible to determine the x or y polarization of the photon arriving at A (because a polarizer at 45 degrees has a 50/50 chance of either passing or blocking both x and y polarized photons).

In this scenario, again, the positions of ALL photons reaching detector B are recorded, but this time the recorded positions will be constrained to the interference pattern. It is not a subsample of photons at B. It is all of them. It is true that with a 45 degree polarizer at detector A, you would only record a subsample of photons at detector A, but these photons could have been either x or y polarized (prior to the polarizer at A) which means you have no which-path information. You would see the interference pattern at B whether you examine all photons at B or even just the ones that coincide with photons detected at A.

If what I have said is correct, then it really DOES mean that you can make a change only only to the configuration of detector A and effect a change in the pattern recorded at detector B.

I believe Membrane Theory will eventually show that Quantum Entanglement is not Faster-Than-Light communication, but is the observed by-product of wave interactions on a seamless hyper-spherical 11-dimensional space-time membrane. These wave interactions are what we perceive as sub-atomic entities. All matter and energy is merely waves on the membrane, and therefore everything is connected to everything else on the membrane. The perception of separate objects or particles is an illusion.

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12. Nov 23, 2010

### Kyle-DFW

If coherency was destroyed by the polarization process (which I have read nothing to suggest it would be), then you would not be able to restore the intereference pattern simply by modifying the detector A configuration. In this case, everything is the same on the detector B side, including the QWP, but the interference pattern returns.

13. Nov 23, 2010

### Joseph14

A QWP provides 2 different speed to pass through the crystal corresponding to a fast polarization and a slow polarization. We will call these P1 and P2.

If light has a random polarization then half of the photons will take the slow route and half the fast route at both slit 1 and slit 2, which will mess up the interference.

Now if the polarizer at detector A forces the polarization to be P1, then photons at slit 1 will always take the fast route and at slit 2 always the slow route so there will be interference. And the opposite will happen for orrientation P2 resulting in interference as well.

14. Nov 23, 2010

### Kyle-DFW

I don't believe the polarizer at A "forces" anything. It either passes the incoming photon or doesn't, based on the photon's incoming polarization. This merely enables you to know the which-path information and should not logically have any effect on the photon behavior or results at B.

Also, since my understanding is that each measurement is taken with a SINGLE PHOTON at B along with its entangled partner at A, it seems that a single photon could not be de-coherent with itself, yet the interference pattern still emerges as these individual photons pile up.

There is nothing I have read that says anything about fast route / slow route having anything to do with whether or not an interference pattern is observed.

15. Nov 23, 2010

### Cthugha

No, it is not that easy, but the webpage you linked obscures the reason for why that is so, because the pictures are somewhat hard to read. If you have a look at the pdf linked at the beginning of the document, you will find that both detectors are not bucket detectors, but only small-area detectors. So if you detect a photon at B, but no photon at A, it does not necessarily mean that the photon was blocked by a polarizer. Your small-area detector A might also just not be at the right position to detect the photon. If you had a large-area detector in that place, you should in my opinion also get no interference pattern or - more correctly - you would integrate over many shifted interference patterns that add up to no pattern at all.

16. Nov 23, 2010

### Kyle-DFW

I have to disagree. Why would Detector A need to be a small area detector? Everything I've seen indicates that A is a bucket detector. If there is something in the PDF to the contrary, please quote it. I didn't see it.

Even if some photons were not seen at A for some sort of positional reason (rather than being blocked by the polarizer) it should be a small number that would not significantly effect the results. Detector A's only job is either absorb the photon as-is, eliminating any which-path information because the polarization was not measured, or to absorb the photon after it passes through the polarizer (if it does), at which point which-path information is available. The spatial location where the photon strikes detector A is irrelevant.

Detector B is a small area detector that moves through space across the potential range of the interference pattern and gives you a count for the number of photons detected at each spatial point in the range. Detector B sits at each position long enough to count enough photons that you get a good sense of the relative number of photons hitting each point.

17. Nov 23, 2010

### Cthugha

The paper says:
"The detectors are EG&G SPCM 200 photodetectors, equipped with interference filters (bandwidth 1 nm) and 300 micrometre x 5 mm rectangular collection slits.
A stepping motor is used to scan detector Ds ."

Both detectors are of equal size. You need to move Ds along to detect all photons. You would also need to move the other detector around to detect all photons on the other side.

Sorry, but this is not a small number. I doubt you will get more than 5% of all the photons at a fixed position of detector A. The exact position of that detector represents a measurement of the wavevector or equivalently emission angle of that photon. Entanglement relies on two photons emitted with well defined sum momentum, but variable magnitude of the momentum of the single photons. Therefore the area on the fixed-detector side which can get hit by photons is quite large. The spatial location where detector A is hit is not irrelevant. You would get an interference pattern at in the coincidence counts at each possible position of detector A, but it would be slightly shifted at each of these positions.

18. Nov 23, 2010

### Kyle-DFW

I don't believe this specific scenario was tested by these particular scientists, but everything I've read leads me to believe you would get interference in this scenario because no which-path information is available without the polarizer.

19. Nov 23, 2010

### Cthugha

The result of exactly this scenario is shown in figure 3. The result is: no interference.

20. Nov 23, 2010

### Kyle-DFW

I'll concede now that the detectors are both small and that a lot of photons are lost at A. I'll further concede to an earlier post that the experiment done by these scientists only records at B when there is a coincidence at A. However, I'm still of the opinion that this doesn't matter because I believe the lost photons don't cause a change in the pattern. They only cause it to take longer for the coincidences to be detected and longer for the pattern to build up.

The which-path information is either present or erased regardless of whether detector A was able to capture the photon. All photons at B will show interference in the absence of which-path information, and no interference in the presence of which-path information, regardless of whether you look at all photons at B or only the ones where you also capture the partner photon at A.

It may be that they only looked at the B photons which were in coincidence with A for some reason such as to eliminate noise photons that might be entering the system from other sources.

How is there going to be an interference pattern in the photons arriving at A when there are no double-slits at A? There isn't.

The guys that did this experiment seem pretty smart to me, and I'd have a hard time believing they could overlook something so seemingly basic if it was really going to somehow impact the validity of their results.

21. Nov 23, 2010

### Kyle-DFW

The documentation is a little ambiguous in that section, but I'm inclined to think that Figure 3 is showing the QWPs being added after the polarizer is already in place as shown in Figure 1.

Whether or not the QWPs do or do not show an interference pattern in the complete absense of the polarizer I think has little bearing on the bulk of the experiment though. I think it would only speak to the question of when which-path information becomes available, and when exactly the wave function collapses. If the QWPs show no interference even without a polarizer, then the mere fact that which-path could be learned from photon A (even if we don't actually bother to polarize and measure it) is enough to collapse the wave function and see purely particle-like behavior at B.

If the polarizer is required to be present (and set to the correct angle) in order to eliminate the interference pattern, then the inference is that wave function collapse does not happen until photon A passes through the polarizer, at which point which-path information becomes available.

The really cool part is that when you read on down the paper to where it talks about delayed erasure, the language seems to suggest that, even though the path at A is lengthened such that photon B is detected before photon A reaches the polarizer, the observed pattern at B will remain consistent with the angle of the polarizer on A.

This is the part of the experiment that gives rise to discussions of quantum retro-causality.

22. Nov 23, 2010

### Cthugha

Having erased which-way information is indeed a neccessary, but not a sufficient condition to see interference. In easier terms of single-photon interference the property defining whether you see interference or not is spatial coherence, which is nothing else but the spread in possible emission angles/photon momenta. Small spread means large coherence and a high visibility of the pattern. This is of course completely opposite to the requirements for having entangled photons, where you want to monitor a large spread of angles. Therefore you get the well-known result that there are no interference patterns in the detections at B alone. To see this pattern, you need two prerequisites:

a) Like in the usual double slit, you need to have both slits open and equivalent, so you do not get which-way information in terms of polarization or other markers.

b) You need to restore spatial coherence. Although the whole emission arriving at detector A is incoherent, you can pick a small subset of higher coherence by just using a smaller detector area. This is like increasing spatial coherence of rather incoherent light by placing a pinhole in the beam. Now the chosen subset of simultaneous detections of this small area at A and the photons at B will show an interference pattern. If you now moved detector A a bit and did the experiment again, you would also see an interference pattern in coincidence, but it would be slightly shifted. You now have a slightly different spread of momenta. This similar to performing a common single-photon interference experiment using a double slit, but moving the source parallel to the axis of the double slit. By doing so, you get a phase difference between the fields originating from the source, but now taking paths of different lengths to the two slits. Therefore the resulting pattern will get shifted. If you now move the source along several positions, record interference patterns for each of these positions and sum them up, you will end up with no interference pattern at all. Exactly the same happens, when you use a bucket detector at A. In fact, you have interference patterns, but you have a superposition of many of them slightly shifted with respect to each other, so you end up with seeing no pattern at all.

23. Nov 23, 2010

### Kyle-DFW

I appreciate exchanging ideas with you since, after all, that's what science is all about. However, much of what you have said does not make sense to me and you haven't really provided any references to support your claims.

I'm going to respond to your last round of comments, but, in the absence of any new information that strikes me as relevant, I'm probably going to end my contribution to the discussion at this time because I fear we are clouding this thread with unsupported ideas of questionable relevance, and making this experiment seem more complicated than it is. This can have the unintended effect of "turning off" future readers of the thread.

The basic undertone of your comments seems to be that you believe the unsupported ideas you have presented are sufficient cause to believe the experimental results obtained by these scientists are somehow invalid. I cannot accept that because the scientific community at large has time and time again upheld the validity of these findings in this experiment and many others like it.

I have read nothing that suggests the required coherence is affected during any of the steps of the experiment or that there is any need to alter/restore the coherence at any point. I would also think that a single photon is always coherent with itself.

It's true that you want to measure a large spread of angles on B behind the slits because this is where the interference pattern will appear or not, but I don't know what "requirements" you are speaking about, nor is it clear what you are saying is in opposition of these "requirements". The only thing "required" to have entangled photons in this experiment is to shoot the laser into the BBO crystal. Eventually a photon will split into two entangled photons that shoot off at 3 degrees from the original laser beam. There are exactly two reasons that entangled photons are used in this experiment: (1) You can send individual photons at the two slits and measure where they land (2) You can know the polarization of photon B by measuring the polarization of photon A without needing to disturb photon B directly, which of course gives you the which-path information.

Again, single photons are arriving at A on each measurement. Unless I'm missing something, single photons are always coherent with themselves. Further, detector A doesn't care about coherence. It only cares about either registering or not registering the arrival of the photon after the polarizer, so the which-path information can be known. The coherence of the photons is also tightly constrained by virtue of using a laser combined with the entanglement process.

I have read nothing from external sources that supports this assertion. Even if true, I fail to see any relevance or importance in this observation. The question we are trying to answer is whether photons (and other subatomic entities) are waves or particles. When we see an interference pattern (regardless of its relative position), we are forced to conclude that a single photon traveled through both slits simultaneously as a wave, interfered with itself, and then collapsed to a particle when it is observed at a discrete spatial point at detector B. When we see no interference pattern, the logical conclusion is that the photon collapsed to a particle before entering the slits and consequently it went through slit 1 or slit 2 but not both.

Sure, if you moved the photon source during the experiment the interference pattern would move and smear the results on detector B, but in the experiment the laser source does not move, and the fact that we are using a laser means we have highly coherent photons traveling in very tight, highly parallel paths. As a result, when the entangled photons emerge from the BBO crystal, they will emerge at angles of 3 degrees from the original laser beam angle with very little variance. The fact that the entangled photons emerge along a very small, tight angular range means that the interference pattern will be highly (but not perfectly) "in focus" and visible at detector B. It also means that detector A need only cover a small angular range in order to capture the bulk of the photons arriving there. The tiny angular variations in the photons that are recorded might result in a slight smearing of the interference pattern, but it will be insignificant. The pattern will still be highly visible and certainly not completely washed out.

24. Nov 23, 2010

### Cthugha

Well, I can only guess on your level of education on this matter and as it is a very specialized issue I cannot really judge what kind of support you need. One of the prime references on this topic is a PhD thesis by one of Anton Zeilinger's PhD students, but unfortunately it has vanished from the web somewhat like 3 years ago and I do not really dare to cite it anymore as it is not freely accessible at the moment.

I see the point that just believing me saying what the results of this thesis are, is not really scientific. Unfortunately my boss also does not leave me the time to redo these measurements on my own (indeed we have better things to do), so I see several reasons not to believe me. But please allow me to give some final remarks.

No, I do not think the results of Walborn et al. are wrong. Just some of the interpretations of this paper in some mainstream-oriented media are. What is claimed in the manuscript itself is perfectly fine.

I am basically just referring to the basic result that single photon interference (like seen in a double slit) and two-photon interference (like seen in DCQE) are complementary. This has been described in detail in "Demonstration of the Complementarity of One- and Two-Photon Interference" by A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, M. C. Teich.
Please note that Saleh and Teich are really big fish in the quantum optics genre.

I agree mostly.

You have to distinguish between a single photon and an ensemble of single photons with varying properties. This distinction is elemental. The coherence of the laser used is essential, but the result also depends on whether you use spontaneous or stimulated parametric down conversion. Unfortunately both can be abbreviated as SPDC.

Really? I do not see any paper underlining this interpretation of this experiment. As I said before the basic PhD thesis by Birgit Dopfer from the Zeilinger group sheds a lot of light on this issue, but unfortunately it was only available in German and is not available on the web anymore. However, one of the basic results was as follows: You can easily distinguish between single-photon interference and two-photon interference. Single-photon interference is directly visible in the photon detections, while two-photon interference is only visible in coincidence detections. That 'Dopfer thesis now showed that you see:

a) single photon interference, if the distance between the BBO and the double slit is large. In this case it does not matter at all what is happening on the other side.

b) two-photon interference, if the distance between BBO and slit is reduced. The explanation I gave explains this transition easily in terms of spatial coherence. How would you explain it?

I know that this challenge is kind of unfair as I am able to understand German and read the original thesis (and not just my transcription) a few years ago, but I am not just making things up here. If you are in doubt, you might be able to retrieve an original copy of the thesis I mentioned from Gregor Weihs from the university of Waterloo as he is now married to Birgit Dopfer who wrote the original thesis. You might also be able to get a copy from Zeilinger himself.

Really? Doesn't that make momentum entangle photons pretty meaningless? I do not really know, where you disagree with me, but as you are asking for references, for example the fact that each of the single beams of a down-converted pair is spatially incoherent is for example discussed in "Fourier relationship between the angle and angular momentum of entangled photons" by A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett (PRA 78, 043810 (2008)).

Please note that Boyd is another one of the big fish in the optics genre and is not just telling random nonsense.

25. Nov 23, 2010

### Joseph14

hmm is this the one.

Someone found it for me a few weeks ago.

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