Delayed quantum eraser: turning off sensor to bring back interference

[Herbascious J]

TL;DR Summary

Can certain sensors be turned off, or omitted, to bring back an interference pattern at the primary sensor?

I've been learning about the delayed-choice-quantum-eraser experiment. To sum up; I imagine a double slit which has behind it a crystal which splits photons into entangled pairs. The crystal sends a photon to the right, from either slit, toward a single sensor (s1) which simply measures that a photon was received and in a pattern, and then the crystal also sends an entangled photon to the left, presumably from the same slit to an apparatus that allows the entangled photon to be detected (s2, s3) based on which slit it passed through 50% of the time, or the entangled photon is reflected into a path which combines both slits into a single censor (or set of sensors, s4 and s5 which cannot determine which slit the photon passed through).

I was watching a laymens video which made the claim that the crystal, in a sense, is making a measurement when the photon passes through it and the entangled pair are created, therefore an interference pattern cannot be made at sensor 1. This was new to me, hearing this interpretation. Part of my confusion is that I am under the impression that sensors 4 and 5 are showing interference, and this seems to contradict the claim that the crystal is collapsing the wave form. My question is; what if sensors 2 and 3 are turned off, or completely removed from the experiment/apparatus? Does sensor 1 still have no interference? I'm assuming sensor 4 and 5 still have interference.

Video for reference:

 

[DrChinese]

I've been learning about the delayed-choice-quantum-eraser experiment. To sum up; I imagine a double slit which has behind it a crystal which splits photons into entangled pairs. ...

First, here is the paper being referred to in the video, easier to simply read it and look at the diagrams and text. This setup is one of the most complicated experiments to understand, and definitely not a good place to start to understand the various quantum concepts involved.

https://arxiv.org/abs/quant-ph/9903047
A Delayed Choice Quantum Eraser

Please note the following:
a) An individual stream of entangled photons (such as those in the B path headed to the D0 detector) do not produce a double slit style interference pattern on their own. Any interference pattern produced in this experiment is a result of coincidence matching between the A stream and the B stream.
b) The "retrocausality" issue is subject to one's interpretation of QM. There is not a single accepted way of describing the underlying mechanism.
c) QM does not respect causal ordering in the usual manner. The statistical predictions of QM are unchanged and independent of what is measured first in experiments with entangled photon pairs. Depending on the assumptions you make, it may appear that there is retrocausality. But many/most scientists deny this.

 

[PeterDonis]

I was watching a laymens video

Pop science videos are not good sources from which to learn actual science. Particularly for this experiment, which involves very advanced aspects of QM.

 

[.Scott]

I was watching a laymens video which made the claim that the crystal, in a sense, is making a measurement when the photon passes through it and the entangled pair are created, therefore an interference pattern cannot be made at sensor 1.

The claim (at 8:33 in the video) is that "the process of creating entangled photons effectively results in a measurement". When the spontaneous parametric down-converter (SPDC - a BBO crystal in the video) splits a particle, there is no energy transfer to the SPDC - nor does that crystal change states.
At this point, if both SPDC outputs were recombnied and projected onto a screen, the screen could show an interference pattern. I think the problem here is primarily with converting what is happening with the math into English narrative. Which-way (ie, which slit) information is now available on both paths, so it is more spread out. But I wouldn't call it "measured".

Part of my confusion is that I am under the impression that sensors 4 and 5 are showing interference, and this seems to contradict the claim that the crystal is collapsing the wave form.

Exactly. What is critical is whether the which-way information has been "harvested".

My question is; what if sensors 2 and 3 are turned off, or completely removed from the experiment/apparatus? Does sensor 1 still have no interference? I'm assuming sensor 4 and 5 still have interference.

Yes. Once a photon lands and transfers its energy, the system has committed to a slit and there will be no interference pattern.
But I should phrase that without the word "once" because the time reference is inappropriate. Here is the better phrasing:
If any part of the photons trajectory (or the daughter photons trajectories) results in which way information being recorded to the surroundings, then there will be no interference pattern observable in any other part of that photon system.

And I won't even say that that is a perfect statement. I recall one experiment where the double slit experiment was conducted with atoms. (which I have not been able to find) Before the atom reach the slits, the experimenters managed to load it with a microwave photon. The interior of the slits were then configured to act like resonant cavities. When an atom passed through, the microwave photon was left behind - marking the which-way information. But when a passage was made between the cavities, the interference pattern was restored.

Edited 9/24 to correct conditions where interference pattern would appear.

 

[Herbascious J]

Exactly. What is critical is whether the which-way information has been "harvested".

Ok, this is facinating to me because, regardless of the various explanations of quantum behavior this does seem counter-intuitive to me. So, if I may press further, can I switch the interference pattern off and on at sensor-zero, only by manipulating the equipment, placed far away let's say, of the other four sensors, involving only the entagled particles? In this configuration, I wouldn't be changing anything physically about the sensor-zero side of the experiment. To be clear, I'm asking if I could create an interference pattern, at sensor-zero, without touching that side of the equipment, so that I don't have to "farm out" or extract selected measurements. Instead I could see clearly an interference, given only that I changed equipment on the other side, that only interacted with the entangled particles, not the particles I'm looking at? I'm trying to ask an objective question that is empirically demonstrable.

 

[PeterDonis]

can I switch the interference pattern off and on at sensor-zero, only by manipulating the equipment, placed far away let's say, of the other four sensors, involving only the entagled particles?

No. This would amount to sending information faster than light, which can't be done. The only way to detect any change made at sensor zero resulting from anything you do with equipment somewhere else is to collect the data and look for correlations in the statistics, which requires you to bring all of the data to one place using mundane slower-than-light methods.

 

[Herbascious J]

No. This would amount to sending information faster than light, which can't be done. The only way to detect any change made at sensor zero resulting from anything you do with equipment somewhere else is to collect the data and look for correlations in the statistics, which requires you to bring all of the data to one place using mundane slower-than-light methods.

This is where my confusion is. It seems like then, that the crystal can't produce an interference pattern, on either side, at anytime. Is that true? Please see Scott's comment here...

When the spontaneous parametric down-converter (SPDC - a BBO crystal in the video) splits a particle, there is no energy transfer to the SPDC - nor does that crystal change states.
At this point, if both SPDC outputs were projected onto a screen, both screens would show an interference pattern. I think the problem here is primarily with converting what is happening with the math into English narrative.

 

[PeterDonis]

It seems like then, that the crystal can't produce an interference pattern, on either side, at anytime. Is that true?

No. But the "interference pattern" might only be detectable by analyzing statistics in the data, not by just looking. That is what @DrChinese meant when he said:

Any interference pattern produced in this experiment is a result of coincidence matching between the A stream and the B stream.

The "coincidence matching" can only be done by analyzing the data after the fact. It's not something you can see immediately on one side of the experiment when you make a change on the other side.

 

[Herbascious J]

No. But the "interference pattern" might only be detectable by analyzing statistics in the data, not by just looking. That is what @DrChinese meant when he said:The "coincidence matching" can only be done by analyzing the data after the fact. It's not something you can see immediately on one side of the experiment when you make a change on the other side.

Ok, so does this mean that if you set up a simple arrangement with the BBO crystal, so that a beam of photons went through a double slit, then immediately into the BBO crystal and the two split beams would be projected onto screens, there would be no interference? But further, if we lift the crystal out of the way of the beam, the beam would then show an interference pattern after leaving the initial double slit?

 

[PeterDonis]

if you set up a simple arrangement with the BBO crystal, so that a beam of photons went through a double slit, then immediately into the BBO crystal and the two split beams would be projected onto screens, there would be no interference?

In this situation you are not measuring which-path information anywhere, so you would see the same interference pattern on both screens: all the BBO crystal is doing is splitting the pattern created by the double slit into two "copies" (but each "copy" only has roughly half of the original photons in it, since each individual photon will only end up on one side).

The whole point of the "quantum eraser" experiment is to make it possible to measure which-path information. That is what prevents the interference pattern.

But further, if we lift the crystal out of the way of the beam, the beam would then show an interference pattern after leaving the initial double slit?

Of course this will be the case since now it's just the standard double slit experiment.

 

[.Scott]

Ok, this is fascinating to me because, regardless of the various explanations of quantum behavior this does seem counter-intuitive to me. So, if I may press further, can I switch the interference pattern off and on at sensor-zero, only by manipulating the equipment, placed far away let's say, of the other four sensors, involving only the entangled particles? In this configuration, I wouldn't be changing anything physically about the sensor-zero side of the experiment. To be clear, I'm asking if I could create an interference pattern, at sensor-zero, without touching that side of the equipment, so that I don't have to "farm out" or extract selected measurements. Instead I could see clearly an interference, given only that I changed equipment on the other side, that only interacted with the entangled particles, not the particles I'm looking at? I'm trying to ask an objective question that is empirically demonstrable.

Sensor zero? You've been calling them "sensor 1" to "sensor 5" even though your video calls them "detector 1" to "detector 5". Here's a screen shot:

So I will guess that you mean "Detector 1".
Detector 1 catches one each of the down-converted photons. It responds equally to photons from either slit. So it does not capture the which way information.
The reason it always shows the spread out pattern is that it is showing the sum of the results from the other 4 detectors. For detectors 2 and 3, this is the spread out pattern because those detectors are capturing which-way information. In the case of detectors 4 and 5, those interference patterns are out of phase with each other. So the sum of those two is just the spread out pattern.
So detector 1 neither captures which-way information nor is able to locally discriminate between photons with mates reaching detectors 2 or 3 (which-way captured) and those with mates reaching detectors 4 and 5 (which-way information remaining uncaptured).

 

[Herbascious J]

In this situation you are not measuring which-path information anywhere, so you would see the same interference pattern on both screens: all the BBO crystal is doing is splitting the pattern created by the double slit into two "copies" (but each "copy" only has roughly half of the original photons in it, since each individual photon will only end up on one side).

I'm going to knit-pick here a little. My understanding of the BBO crystal is that it is is not directing individual photons to either side 50/50, but instead each photon is split into two identical photons of half the momentum. So, each pattern has the full number of photons on each side that entered the crystal, and further the frequency of light would drop an octave resulting in a lower energy beam. This is something I've never heard directly addressed, but it seems like it would make a difference in how the whole experiment is behaving. I'm not sure.

 

[Herbascious J]

Sensor zero? You've been calling them "sensor 1" to "sensor 5" even though your video calls them "detector 1" to "detector 5". Here's a screen shot:

My apologies, I was attempting to convert to a convention mentioned above. Yes, I mean sensor/detector 1.

The reason it always shows the spread out pattern is that it is showing the sum of the results from the other 4 detectors.

I understand that detector 1 must be showing the same results as the sum of the other four detectors. It seems, from other discussions above, that the BBO crystal can in fact sustain an interference pattern on both sides of the split beam, given there is no which-way information being recorded. The only difference between this, and the eraser experiment, is that on one side of the beam split, the equipment is being rearranged to have multiple detectors. What's strange to me is how can this rearrangement on one side, collapse the wave function on the other beam?

 

[PeterDonis]

My understanding of the BBO crystal is that it is is not directing individual photons to either side 50/50, but instead each photon is split into two identical photons of half the momentum. So, each pattern has the full number of photons on each side that entered the crystal

Yes, sorry, I misspoke. Each output beam has half the energy of the input beam, but the same number of photons. (Of course this is a heuristic description since the states involved are not eigenstates of photon number, but the description is basically correct in terms of expectation values.)

 

[PeterDonis]

The only difference between this, and the eraser experiment, is that on one side of the beam split, the equipment is being rearranged to have multiple detectors.

No, that's not the "only" difference. The arrangement on that side in the eraser experiment has the detectors set up in such a way that, on some runs, the detector readings give which-way information. It's not enough just to have "multiple detectors"; they have to be arranged so that which-way information is provided.

 

[DrChinese]

1. My understanding of the BBO crystal is that it is is not directing individual photons to either side 50/50, but instead each photon is split into two identical photons of half the momentum.

2. So, each pattern has the full number of photons on each side that entered the crystal, and further the frequency of light would drop an octave resulting in a lower energy beam.

3. What's strange to me is how can this rearrangement on one side, collapse the wave function on the other beam?

1. The entangled photon pairs exit the BBo crystal (as implemented here) a few degrees off angle, headed in opposite directions. They could either take the A slit path or the B slit path to get to the crystal. The alignment is such that the path taken (A or B) is not distinguishable. And yes, you can consider the output as 2 identical entangled photons with half the momentum, or as a system of 2 entangled photons - which is sometimes called a biphoton. Note that the output photons need not have exactly the same momentum, but will be very close to that due to conservation rules.

2. Most photons entering the BBo crystal do not downconvert. Perhaps 1 in 100 million will do so. The others go straight through and do not participate in the experiment.

3. The term "collapse" can arouse a lot of debate around here, as it is unknown whether collapse is a physical process; and if so, what is the precise mechanism.

Used as you have (in a casual sense): it is not demonstrably true that collapse first occurs on one side and then causes collapse on the other. That implies a causal order, which is not present in quantum theory. If collapse is physical, then no one knows when, where or how it occurs. Ordering of measurements does not affect the statistical outcomes (i.e. the quantum predictions do not change). So anything you say about that is an assumption which has no experimental or theoretical basis. So usually, the term is used as a convenience in descriptions.

 

[PeterDonis]

how can this rearrangement on one side, collapse the wave function on the other beam?

As @DrChinese says, "collapse" is a problematic term, because different QM interpretations mean different things by it. Discussion of interpretations belongs in the interpretations subforum, not here.

As far as the basic math of QM is concerned, i.e., with actually making predictions, "collapse" is just a mathematical thing you do when you know the result of one measurement, in order to predict the results of future measurements. It's not claimed to be an actual physical event.

 

[Herbascious J]

If I may ask one final question. Is there some experiment where both sides of the BBO split beam are showing interference, and then, only on one side, is the equipment rearranged so that which way info is now known, and because of this, there is a loss of interference on the other side of the experiment? I hope I'm making sense, this is still a little above me. Thank you this thread has been really helpful.

 

[DrChinese]

If I may ask one final question. Is there some experiment where both sides of the BBO split beam are showing interference, and then, only on one side, is the equipment rearranged so that which way info is now known, and because of this, there is a loss of interference on the other side of the experiment?

Good question... No, there is no such experiment because that doesn't happen. See figure 2, or equation (4). Otherwise FTL signaling could be implemented.

https://courses.washington.edu/ega/more_papers/zeilinger.pdf

 

[vanhees71]

First, here is the paper being referred to in the video, easier to simply read it and look at the diagrams and text. This setup is one of the most complicated experiments to understand, and definitely not a good place to start to understand the various quantum concepts involved.

https://arxiv.org/abs/quant-ph/9903047
A Delayed Choice Quantum Eraser

Please note the following:
a) An individual stream of entangled photons (such as those in the B path headed to the D0 detector) do not produce a double slit style interference pattern on their own. Any interference pattern produced in this experiment is a result of coincidence matching between the A stream and the B stream.
b) The "retrocausality" issue is subject to one's interpretation of QM. There is not a single accepted way of describing the underlying mechanism.

At least standard QED tells you that there is no "retrocausality" whatsoever, and QED is the only successful theory of the electromagnetic field and its interactions with matter, and this success is overwhelming. I'd say that's very close to the single accepted way of describing the "unerlying mechanism". The "underlying mechanicsm" of everything (except the gravitational interaction) is today understood in terms of relativistic quantum field theory, which obeys the causality structure of Minkowski spacetime by the assumption of locality of interactions and microcausality.

c) QM does not respect causal ordering in the usual manner. The statistical predictions of QM are unchanged and independent of what is measured first in experiments with entangled photon pairs. Depending on the assumptions you make, it may appear that there is retrocausality. But many/most scientists deny this.

Taking into account that the causality structure of relativistic spacetime is respected by QED, this independence of the order of measurements in this experiment confirms this very construction of the theory obeying microcausality, i.e., that space-like separated events are not causally connected. There is thus no retrocausality at all.

The possibility of postselecting subensembles in the described way in this experiment is due to the fact that the photon pairs created in either of the slits are entangled.

 

[TheHutch]

I know I'm rather late to this thread, for which I apologise, but I had the same question as Herbascious J - or to put it another way, if the delayed choice apparatus is entirely removed so the idler photons just head off into space and do not interact with anything, what is seen at the signal detector?

After reading this thread and the more I study the original paper, (and I'm not quite up to the maths), the more I doubt what is going on here - I'm not convinced the interference patterns shown are anything to do with double slits!

I was always puzzled why the two interference patterns associated with the two quantum eraser paths are out of phase; in a standard double-slit experiment the position of interference fringes should be determined simply by the geometry of the apparatus and the wavelength of the photons.

The paper says this is somehow explained in the maths, but I can't follow it. Instead, I'm trying to find a conceptual picture of what is going on and perhaps someone can tell me where I am going wrong:

The paper claims that for idler photons where the 'which path' information is erased, then an interference pattern is seen for the corresponding entangled signal photons. This is true for the two erasing detectors individually, but not when taken together, as their corresponding interference pattens are exactly out of phase and add up to a simple smudge. So it is not the fact of erasure that is making the difference, it is the fact of which of the two 'erasing' detectors observes the idler photon.

It strikes me that a better explanation of what is going on is that the two erasing detectors are actually detecting phase differences of the idler photons generated at the two separate slits (i.e. acting as an interferometer) and so by implication the phase difference of their corresponding entangled signal photons. Of course the interference patterns of those two subsets of the signal photons will be shifted. And for the two non-erasing detectors - well they are not detecting phase, so their corresponding photons will have random phase distributions and not give rise to interference patterns.

But... how can there be a phase difference in photons passing through a double slit experiment?

DrChinese above says that "Perhaps 1 in 100 million will [downconvert in the BBO crystal]." If that is true, then it would be incredibly unlikely for a single input photon to be downconverted at both slits (in superposition) and what we are really seeing is a single pump laser generating two separate light sources, one at each slit. The laser might be a nice coherent beam of photons, but if those generated light sources are at all diffuse, then phase differences will be the consequence, surely? From the description in the paper, the slits are about 1000 wavelengths apart and the crystal is about 400 wavelengths thick (after downconversion). I don't know much about type-II phase matching nonlinear optical crystal BBO crystals, but I wouldn't be surprised if that gives scope for variation in the origin of generated entangled pairs, with corresponding variations in phases.

In summary, this doesn't seem to be a double slit experiment at all, instead is seems to be a double light source experiment showing nice interferometry and entanglement effects, but not quantum erasure.

I find this really disappointing, so please tell me where I am wrong!

 

[TheHutch]

For the record, I just came across a paper whose title says it all: "The ‘Delayed Choice Quantum Eraser’ Neither Erases Nor Delays" R.E. Kastner 2019 available here: https://arxiv.org/abs/1905.03137

This argues at a fundamental level that entangled photon experiments don't prove what they appear to claim and the effects seen are down to statistical correlations. So the answer to the question in this thread is no - you will never see an interference pattern without actively selecting a suitable subset of photons to record.

I'm still puzzling about why the interference fringes are exactly out of phase - this seems to be demanded by the maths in the Kastner paper. There must be some fundamental mechanism at work here, perhaps a very delicate 'tuning' of the path lengths in the apparatus? Does anyone know if the experiments fail completely (in terms of seeing interference fringes) unless the path lengths are exactly right?

 

[PeterDonis]

I'm still puzzling about why the interference fringes are exactly out of phase

That is a consequence of entanglement, and it is a key reason why many physicists do not accept an explanation along the lines of "it's all just statistical correlations".

 

[TheHutch]

Thanks, but can you elaborate please? I have no problem with the idea of entanglement, but in a Young's slit experiment, the position of the interference fringes is determined purely by the geometry of the apparatus, surely? This implies that for fringes to be shifted when using the same set up, there needs to be a relative phase shift in a photon traveling on one or other of the two paths. In Walborn et al 2008 I can see that the orthogonal quarter wave plates in the two paths might achieve this by rotating the polarisations, but in Kim et al 1999 there is not supposed to be any difference at all in the paths... yet an out of phase pattern is seen when correlating with one vs the other 'eraser' detectors.

 

[PeterDonis]

or fringes to be shifted when using the same set up, there needs to be a relative phase shift in a photon traveling on one or other of the two paths

No, there just needs to be a difference in the overall phase of one set of photons vs. the other. The two interference patterns that are out of phase are produced by two different sets of photons with orthogonal polarizations; the difference in polarizations is the phase shift. But the difference in polarizations is itself a consequence of the entanglement between the signal and idler photons.