Delayed Choice Quantum Erasure Demystified

[bruce2g]

Delayed Erasure Demystified

Delayed choice quantum erasure experiments claim to produce a 2-slit interference pattern in a beam by 'erasing' the which-path information contained in an entangled beam. There's an implication that the erasure happens after the interference is measured, and that some sort of 'backwards time' phenomenon has occurred. I believe that if you look carefully at how the erasure is accomplished -- the two idler beams go through a beam splitter and onto two detectors -- then the normal direction of causality can be restored.

The basic argument is that you can look at the data and say that the erasure in the idlers brings out the interference in the signal photons (the authors' argument), or you can say that the X position of the signal photon determines the phase of both the signal and the idler, and this determines the probability that the idler will go to one or the other detector (my argument).

Basically, I'm going to make 4 points, and then elaborate on them.

MY POINTS

Point 1: In his delightful book "The Fabric of the Cosmos," Brian Greene describes the classic delayed choice quantum erasure experiment on page 196. Unfortunately, in his diagram, he oversimplifies the setup by omitting the coincidence counts between the signal detector D0 and and the idler detectors D1 and D2. This is a critical omission, because --

Point 2: The interference pattern only appears in the signal photons after the erasure if you discard half of the signal photons, and then look at the ones that remain. You have to either discard the signal photons which are coincident with idlers detected at D1, or else you have to discard those coincident at D2. Then you see the interference. This is why you need to (classically) combine the detection data of the signal photons with the detection data of the idler photons in order to see the interference.

The above points have been make on this forum before. I have 2 new points to make:

Point 3: Interference fringes show up as increasing and decreasing coincidence counts as a function of D0's x position behind the double-slit. The coincidence count is performed between D0 (the signal photon detector behind the slits) and either D1 or D2. As you move detector D0 (i.e., as you vary x), the coincidence counts with D1 go up and down to reveal an interference pattern. Similarly, the coincidence counts at D2 go down and up to reveal a complementary interference pattern. Figure 1 has a simplified diagram of the experiment.

There is another way to look at these data: you can also say that the probability that an idler is coincidence-counted at D1 is a function of the X position at which the signal photon is detected. As you vary X, the idlers will first tend to be detected at D1, but then the probability will move towards D2 as X increases, and then back to D1. This means that the beam splitter, which combines the two idlers and erases the which-path information, sends the combined idler beam photons to either D1 or D2 with a probability which depends on the X position at which the signal photon was detected. In other words --

Point 4: There is an entanglement between the signal photon's x and the idler's probability of registering at D1 or D2 (which is based on the relative phase between the idler beams when they reach the beam splitter). This is shown in figure 2. There, I have taken the data from the charts in the original article, and combined the D1 and D2 data using the following formula: for a given X, p(D1|X) = (D1 count when D0=X) / (D1 count when D0=X + D2 count when D0=X).

Thus, we see that the 'erasure' can be interpreted as another aspect of the entanglement (in this case the phase entanglement) between the signal and idler photons.

I mention these things because some people seem to think that the delayed choice quantum erasure experiment reaches back in time and somehow rearranges the signal photons into an interference pattern after the erasure at the beam splitter. This does not happen. If the signal photons are detected first, then you see the interference pattern emerge because the point at which a signal photon is detected determines the relative probability that the idler will subsequently be detected at D1 or D2.

References:

The Kim, Kulik, Shih and Scully experiment, is described in the paper 'A Delayed Choice Quantum Eraser' at http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9903/9903047.pdf and also nicely annotated at http://www.bottomlayer.com/bottom/kim-scully/kim-scull

Bruce Zweig

 

[cesiumfrog]

Given the point where D0 detected the signal photon, how would you go about calculating the probability of detecting the corresponding idler photon in your D1 versus D2?

 

[Farsight]

Thanks for that, Bruce. I thought there was something odd about the plot counts on the earlier thread. I'll reread.

This thread next door has got my attention too:

https://www.physicsforums.com/showthread.php?t=133929

 

[bruce2g]

Given the point where D0 detected the signal photon, how would you go about calculating the probability of detecting the corresponding idler photon in your D1 versus D2?

I did it using the data in the original paper: Fig 3 gives joint detection at D0 and D1; Fig 4 gives it for D0 and D2. Take X=1.0: Fig 3 gives 45 D0-D1 counts, and Fig 4 gives 80 D0-D2 counts when X=1.0. So, given that there is a joint detection and X=1, P(D1) = 45/(45+80) = .36, and P(D2) = .64.

In the paper, they derive a formula for the coincidence rates R01 and R02 as a function of X (eq 10). So, for a given X, P(D1) = R01/(R01 + R02), and P(D2) = R02/(R01+r02) (I'm assuming that R012=0, which has been verified to be negligible). Theoretically, p(D1|x) = cos^2(kx), where k = pi*d/lambda*f (d is distance between slits (0.7 mm), lambda is 702.5 nm, and f is the focal length of the lens, which is not given). Theoretically, P(D1) should go down to 0, but .25 seems to be the lowest value observed.

Bruce

 

[RandallB]

In his book "The Fabric of the Cosmos," Brian Greene describes …. quantum erasure...on page 196. Unfortunately……omitting coincidence counts between the signal detector ……and idler detectors ……is a critical omission, because --

I am not a fan of B Greene and Strings, but I don’t think you can claim he made a “critical omission” in this description. No matter how one explains this it can be hard to follow; but I think he did OK if maybe only fair job of it.
He describes “coincidence counts” instead as a “subset of data points” in the middle of page 197. Plus more than once he makes a big point that date learned in the future does not change the data already documented to address the “reach back in time” issue in the following page or so.

So I have no problem with his complete effort there.

I like your re-graphing the data in a more meaningful way – I think you make a significant point on relating an interference affect at the last beam splitter to position at the signal detection as the cause for producing the interference in the data.
Your observation on the 25% vs. 0% intensity issue seems significant to me as well.

 

[bruce2g]

I am not a fan of B Greene and Strings, but I don’t think you can claim he made a “critical omission” in this description. No matter how one explains this it can be hard to follow; but I think he did OK if maybe only fair job of it.
He describes “coincidence counts” instead as a “subset of data points” in the middle of page 197. Plus more than once he makes a big point that date learned in the future does not change the data already documented to address the “reach back in time” issue in the following page or so.

So I have no problem with his complete effort there.

Thanks for your comment. If you read Greene's description carefully, then you're right, he does say that you need to look at the photons associated with the idler detector to see the interference. I guess it was initially hard for me to digest that fact, since he doesn't give any reason for why you have to look at just one of the erased detectors, but not both, and also because in the diagram the connection from the detector to the screen is not present.

I like your re-graphing the data in a more meaningful way – I think you make a significant point on relating an interference affect at the last beam splitter to position at the signal detection as the cause for producing the interference in the data.
Your observation on the 25% vs. 0% intensity issue seems significant to me as well.

Actually, it was my curiosity about why you need to look at just one idler detector that led me to reexamine the data and that's how I saw that the idler eraser is just an interferometer whose probability of going to D1 or D2 is a function of the signal's detected X.

I'm still not100% sure how the phase of the idlers gets entangled with the detected signal's X. Intuitively, it seems to me that the X of the signal imples two different distances from slit 1 and slit 2, hence a phase difference, and that the phase difference is reflected in the detection probabilities of the idlers.

 

[kvantti]

And now, since you've demystified this, how about demystifying a regular double-slit experiment? You should be able to do this because the delayed choice doesn't differ a lot from it; the delayed choice quantum eraser is just a variation of the original double-slit and its results are completely predictable from the mathematical formulation of QM.

So again, it all comes down to the interpretation you use to interpert the results of a certain experiment.

 

[bruce2g]

My own point of view, which is a sort of ultra-orthodox Copenhagen view, is that a wave goes through the two slits, and that the photon doesn't even really exist until it is detected. When the wave interacts with a detector, it does so in increments of energy = h*nu; because of the quantization, we say that a 'particle' has interacted with the detector. But there was really no evidence that a particle existed until there was an interaction with the detector.

It's possible to extend this point of view, and say that the wave interacts with the detector in a way that makes us think that a particle exists, but the particles are really just mental constructs that make it easy to organize the data.

 

[selfAdjoint]

My own point of view, which is a sort of ultra-orthodox Copenhagen view, is that a wave goes through the two slits, and that the photon doesn't even really exist until it is detected. When the wave interacts with a detector, it does so in increments of energy = h*nu; because of the quantization, we say that a 'particle' has interacted with the detector. But there was really no evidence that a particle existed until there was an interaction with the detector.

It's possible to extend this point of view, and say that the wave interacts with the detector in a way that makes us think that a particle exists, but the particles are really just mental constructs that make it easy to organize the data.

I am really sympathetic to your nominalism, but even if all of our theories are just "circles of beliefs", don't you agrree we should try hard to make those circles self-consistent and coherent? In particular if "the wave" does all these things in the world, then that seems to entail that it exists in the world, and if so, what in hell is it?

 

[bruce2g]

I am really sympathetic to your nominalism, but even if all of our theories are just "circles of beliefs", don't you agrree we should try hard to make those circles self-consistent and coherent? In particular if "the wave" does all these things in the world, then that seems to entail that it exists in the world, and if so, what in hell is it?

Thanks for asking such a provocative question. I have a couple of thoughts on it.

First, for a photon, there's a relationship between Maxwell's equations and Schrödinger's equation. The photons manifest as measurable effects of the electromagnetic wave. The interference can be derived from the electromagnetic wave. However, each photon also has its own quantum wave packet, and these waves have the same frequency as the EM wave, and so could also produce the observed fringes.

Does this make sense so far?

Bruce

 

[RandallB]

Delayed Erasure Demystified

... and also nicely annotated at :yuck:

Bruce
I noticed your link to the annoteted notes link in the OP didn't work and found the correct link to http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm"
so others can find as well. They are good you may want to read them again.

Also I'm with selfAdjoint, and wonder “what in hell is it?” as most of us in this forum at least are not interested in “mental constructs”.
So, while here, it may be better to try another direction.

 

[selfAdjoint]

So, while here, it may be better to try another direction.

Two ideas, not for assertion, just for discussion. They are both intended to preserve the mathematical formalism.

1. CarlB described his pretty approach based on propagations of a dislocation in a crystal, with spacetime playing the part of the crystal. Perhaps he will lay it out for us here.

2. I have been toying with the idea of thw QED vacuum as a "quantum ether"; not the old mechanical kind but capable of a number of different kinds of states, complex, spinorial, etc. (perhaps to be unified in some Clifford or other algebra). The amplitude propagates through this and interacts with more or less locality.

Either or both of these might easily be shot down by tomorrow, but tonight we brainstorm!

 

[RandallB]

Brainstorming options:

ideas, for discussion …. intended to preserve the mathematical formalism.

2. …toying with QED vacuum as a "quantum ether" ……..

I like your thinking; looking to a form of ether more like the intangible Aether Einstein spoke of in the 20’s. But I’ve decided the “Real” solution needs to come from someplace else; the Erasure Model needs to be considered, but may focus to much on the 'mathematical formalism'.

And I’ve about decided that worrying about that 'formalism' is the wrong thing to do – it can take care of it self. Don’t get me wrong the mathematical formalism give accurate predictions of what reality will be – but that is not the same as a correct description of reality.

I think we are not even asking the right question that can help explain things in a real tangible way - and worse how do you pick which ‘paradox’ or unexplained phenomena to look at for a new question?

 

[bruce2g]

I am really sympathetic to your nominalism, but even if all of our theories are just "circles of beliefs", don't you agrree we should try hard to make those circles self-consistent and coherent? In particular if "the wave" does all these things in the world, then that seems to entail that it exists in the world, and if so, what in hell is it?

I had a couple of additional thoughts about the wave: thanks to you and Randall for thinking about it.

First, the erasure results indicate that the SPDC's do not just turn one photon into two entangled ones. The SPDC's also appear to turn one wave into two: the beam splitter at the end of the idler path receives two waves, one for each slit that the idler could have gone through. Depending on the phase difference between the two waves at the BS, the idler photon will tend to register at either D1 or D2; this probability correlates with the X position registered at D0 by the signal.

This makes me wonder what's going on inside the SPDC's: are they making particles out of particles, or waves out of waves? Or, by the same token, when a photon decays into an electron and a positron, what happens to its electromagnetic wave? Does it decay into two matter waves?

And, interestingly, researchers on Bose-Einstein condesates matter-of-factly refer to matter waves all the time, so it seems that they do 'exist.'

These are just some offhand thoughts, let me know if they sound interesting.

 

[bruce2g]

Bruce
I noticed your link to the annoteted notes link in the OP didn't work and found the correct link to http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm"
so others can find as well. They are good you may want to read them again.

Thanks for pointing that out. Unfortunately, I can't edit my original post to correct the URL, so hopefully anyone interested will read down to your post.

Interestingly, the author of the bottomlayer.com post thinks that the signal photons look into the future to see whether their path information is erased or not, and then interfere or not based on the future event. I guess that's another reason I did my analysis.

 

[wm]

I am really sympathetic to your nominalism, but even if all of our theories are just "circles of beliefs", don't you agrree we should try hard to make those circles self-consistent and coherent? In particular if "the wave" does all these things in the world, then that seems to entail that it exists in the world, and if so, what in hell is it?

How about this? Space-time is an elastic medium with a temperature of zero-K; the conclusion re its elasticity being drawn from the space-time distortion associated with the presence of mass-energy (per general relativity); the conclusion re its temperature being drawn from the absence of mass-energy losses due to motion through it.

Thus the motion of mass-energy in space-time will generate real waves in space-time; the subtle effects of such waves being demonstrated in one-versus-two slit experiments, closed-versus-open arms in interferometers, etc.

 

[RandallB]

Interestingly, the author of the bottomlayer.com post thinks that the signal photons look into the future to see whether their path information is erased or not, and then interfere or not based on the future event. I guess that's another reason I did my analysis.

That is why I think your work there is useful, a good collection and interpretation of data in a that shows the authors opinion that “signal photons look into the future” is frankly ridiculous. As your data shows it is only the fixed results of the signal photons compared statistically by someone in the future with the fixed results found in the idler that builds a pattern or not. No implication of a change of action by the signal based on a future result is implied at all. I would see that as a good QM evaluation of the information, BUT you also highlight the measurement of the pattern did not show as a complete Young’s double slit result. Your example showed that the pattern does not give “Dark” spots but about 25% dimmed spots. As I said before a significant point IMO.

Allow me to restate your observations in your latest post that may have your own comments make most sense to you. Think of it a photon splitting in two by the PDC but a photon acting as wave splitting two photons acting as each acting as a wave – BUT importantly in doing so it must be considered as have been “measured” by this intervention. Then as you said the other side need be considered an invisible wave (extra dimension or something be preserved as a guide way) also being split in two by a PDC and “measured as well. You have four waves your working with, and combining 2 elements of opposite PDC results to find no pattern. But when that pattern is divided based on the other two elements being combined a you get your 25% dimming pattern.
Your should consider this as a BM view looking at the problem with guide waves and giving the same result as QM.

But what to do with it? – can some additional information or indication be teased from this by trying to explain why the pattern only came back at 25%? Certainly the PDC’s acting as a ‘measurement’ destroying the pattern is involved. But how was 25% of the pattern able to be recovered and why only 25%.
Maybe this is in the area of a NEW question.