A way aroung determining which-paths in interference patterns?

[Gothican]

In Brian Greene's book 'The Fabric of the Cosmos' he introduces an experiment called the "delayed-choice quantum eraser". This was really a magnificent experiment at first sight but pretty unclear when I was done reading the results.
The experiment basically goes like this:
In each path that the photon can go through towards the detector are positioned photon splitters (called down-converters), that take photons as input and produce two photons, each with half the energy.
One photon (called the signal photon) continues toward the detector, and the second (called the idler photon) goes through a different path:
in this path the photon has a 50% chance of being detected (and then we will know the path the original photon went through), and 50% percent chance of being lost (with the result of us never knowing which path the original photon took).
The result is perfect correlation between the interference-pattern signal photons and the undetected idler ones, and vice-versa.
That's it. for those who didn't understand it fully can read this article:
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser"

Now, let's say we delay the measurement of the idler photon until after the signal one goes through - if the signal photon already decided upon it's state (having made an interference pattern by going through both slits, or choosing only one of the slits and making up two lines of the detector), then how can it know if we will decide to take away the 50-50 chance of it's idler photon getting detected, and directly decide to detect it or not?

Thanks in advance,
Gothican

 

[DrChinese]

Now, let's say we delay the measurement of the idler photon until after the signal one goes through - if the signal photon already decided upon it's state (having made an interference pattern by going through both slits, or choosing only one of the slits and making up two lines of the detector), then how can it know if we will decide to take away the 50-50 chance of it's idler photon getting detected, and directly decide to detect it or not?

Seems like an impossibility! But there you are...

In experiments of this type: You can logically deduce that Alice's result occurred before Bob's measurement was decided - usually requiring Alice's result to conform to some rule. It seems like a paradox! But you must compare both results to notice the predicted correlation. Interestingly, in the quantum world, the order of the observation of members of an entangled pair is not important.

If you want a picture to help visualize things, this may help: It is "as if" the context of the experiment - how Alice is measured and how Bob is measured - is known to the entangled particle pair at inception. That is true regardless of the sequence of the observations. So you could say (remember this is "as if") a future context - even where portions of the context are themselves spacelike separated and/or occurring at different future times - influences an event in the present. Now, the quantum formalism does not include this "informal" description. But it is fully consistent with what actually happens. And yes, it is strange. But it makes it easy to comprehend those strange results!

 

[rrogers]

As a EE I would like to offer a different interpretation; which I have never seen invalidated. Imagine the interference pattern as encoded such that the signal is indistinguishable from noise; then split and sent to two observers. Both observers would see pure noise but a cross-correlation would recover the original signal.
Consider the experiment in this light; except get rid of the coincidence counter and record hits. Now the hits at detector D0 occur at random times, but when various masking data sets from the other detectors are applied to these time series one either gets uncorrelated noise, or the original pattern. The interference pattern will only be recovered when both correlated copies are compared. Subsequent beam splitters and mirrors merely reencode the time series and may or may not reconstruct it depending upon their individual paths.
Actually one has to talk about transmitting the spatial phase information by randomly sampling it in time; but that's too hard for me.

I would appreciate it if anybody finds problems with this reasoning. That would mean I have to go back and rethink my understanding of QM; which in fact is on shaky ground to start with.

Ray

 

[rrogers]

A problem with my previous reasoning is that it implies the "information" is encoded at the source. I know that the noise encoding is done at the detector. That is a famous experiment/theorem proposed by Bell. This is also something that has a mathematical basis; but is hard to wrap my head around. None the less, an elaboration of the "delayed choice" experiment would reveal it's truth in subsequent data analysis; presuming the time series are recorded for subsequent analysis.

Ray

 

[Gothican]

Thanks--but I don't understand--why is there a need to cross-correlate? where does the "noise" come from? is it because of the other particles whose paths have been definitively ascertained? if so, why not just get rid of particles pathways that can be definitively ascertained, and try the delayed-choice experiment without them?

 

[DrChinese]

Thanks--but I don't understand--why is there a need to cross-correlate? is it because of the other particles whose paths have been definitively ascertained? if so, why not just get rid of particles pathways that can be definitively ascertained, and try the delayed-choice experiment without them?

Coincidence counting (cross-correlation) is how the "which path" subset is segregated from the "non-which path" subset. I think the use of the word "noise" can be confusing. You could call the random values "noise" and then it makes more sense, but I prefer to drop the word "noise" as that implies some kind of flaw in the experimental setup.

 

[JesseM]

Thanks--but I don't understand--why is there a need to cross-correlate? where does the "noise" come from? is it because of the other particles whose paths have been definitively ascertained? if so, why not just get rid of particles pathways that can be definitively ascertained, and try the delayed-choice experiment without them?

Look at this part of the wikipedia article you linked to:

However, it should be noted that an interference pattern can only be observed after the idlers have been detected, when the experimenter plots either the subset of signal photons at D0 that are entangled with idlers that went to the detector D1 (the D0/D1 coincidence count), or the subset of signal photons at D0 that are entangled with idlers that went to the detector D2 (the D0/D2 coincidence count). The total pattern of all signal photons at D0, whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons;[2] one can get an idea of how this works by looking carefully at both the graph of the subset of signal photons whose idlers went to detector D1 (fig. 3 in the paper) and the graph of the subset of signal photons whose idlers went to detector D2 (fig. 4), and observing that the peaks of the first interference pattern line up with the troughs of the second and vice versa (noted in the paper as 'a $$\pi$$ phase shift between the two interference fringes'), so that the sum of the two will not show interference.

The point is, even if you were to remove the two beam-splitters BSA and BSB in the diagram from the wikipedia article, so that none of the photons would go to the which-path preservering detectors D3 and D4 and all of them would go to the which-path erasing detectors D1 and D2, then even though you'd see interference in the D0/D1 coincidence count and in the D0/D2 coincidence count, the total pattern of signal photons at D0 would look like the sum of these two (since some signal photons have their idlers detected at D1 and other signal photons have their idlers detected at D2), and because of the phase shift in the two interference patterns (the peaks of one lining up with the troughs of the other), their sum looks like a non-interference pattern.

 

[rrogers]

Imagine a signal, a wavelet, passed down a wire whose exact time is unknown. A probability wave packet. You don't get to know an event (time of arrival) until you detect it. A second entangled wave packet is sent along an alternate route. They are only in phase, out of phase, if the two paths are matched. If you play with the packet, observe it, you distort it. (I'll make an exception to the usual interpretation below). Now you don't get to "see" the actual packet; only detect an event. A time signal from the detector.
The "interference" pattern is spread out over time and space. To see if you have reinforcement/cancellation you have to mask the received "signal" with the "idler" to extract the events that are correlated. The resolution of the wave packets to detector signals is done at the detector via the probability wave function calculation.
In the split slit experiment the masking (enforcement/cancellation) is done physically at the interferometer. It's interesting that the packets can cancell at certain spots but the actual total energy is preserved. The realization point is just moved around by the probabilitiy wave interference; but the total probability is preserved (=1 in an ideal experiment) as is the energy. The energy conservation is an exotic formulation in QM which is hard to make sense of except in the light of preserving the PDF and energy simultaniously (IMHO but I am certainly not an expert).
In the delayed experiment the sidetracked wavelets are essential for the experiments purpose. You have four "idler" paths of equal magnitude and you want to demonstrate that 2:4 of the paths have the correlation between the paths restored, and that 2:4 have been destructively tampered with. Thus you need to have twice (or four if you are picky) as many raw photons as scattered ones at the "signal" detector; and you are picking out the events you are interested in by using the other "idler" path. Then you can only pick out the interesting events when you have all of the information collected; either by a coincidence counter or post processing.
Concerning the usual double slit experiment and tampering with the path. They say that the correlation is destroyed when one path is detected. I doubt this in the sense that if the other path was brought around to the path detector you could reconstruct the interference and the path detector; with sufficient ingenuity. Just a personal opinion.

Does this make sense?


Ray

 

[DrChinese]

...Concerning the usual double slit experiment and tampering with the path. They say that the correlation is destroyed when one path is detected. I doubt this in the sense that if the other path was brought around to the path detector you could reconstruct the interference and the path detector; with sufficient ingenuity. Just a personal opinion.

Does this make sense?


Ray

In principle, neither entangled twin imparts any additional information whatsoever over what one alone provides. You could probably put 2 photons back in phase after a polarization observation on one (without observing the other), but this again is redundant information; and so there is nothing mysterious about that.

However, you CAN use an entangled twin to extract information about *commuting* observables that you might not otherwise be able to extract effectively. Examples would be spin and position observables.

 

[rrogers]

Your quite right about the noise and information terms. I was using them very loosely. OTOH being precise would get quite technical rapidly. I was generically speaking, in that the interference pattern contains certain information about the experimental structure which is missing from a single shot path event.
Rephrasing the path detection reasoning. If you were to put up a polarizer or some such in one path there would be a reaction during the path detection (I can't speak to Penrose's bomb/dud detection scheme); if you were to also take the alternate path photons and combine them in the same reaction/detector then you should have the same type of inference effects. That's the basis for my statement; that you have just moved the interference to a different detector. Of course you can always miss the detector in either case; but theoretically you should be to combine the measurements. In my opinion.
Every time I read Penrose I am overawed. I have to get over that, and get critical. Of course QM is just a hobby of sorts. I can post an appropriate cartoon about me an QM.

Ray

 

[Gothican]

Let me see if I understand, we can't tell the two types of signal photons apart (those whose idlers' which-paths were detected, and those that weren't) at the screen, unless you correspond between the idlers and the signals.. That way you don't change the past - you just interpret it.

But let's say that just before the idlers get to the junction (in which they get "which-path"-ed, or erased) you decide to detect them all - that way you'll be able to tell between the interference pattern and the two lines - because they all were "which-path"ed!
In other words, if you detect all the idler photons' which path, then there shouldn't be any interference pattern!

By this reasoning, you could clearly discern whether there is an interference pattern or just two solid lines on the screen. And, if you can do this (at least till you can show me why my reasoning is flawed) you have the ability to change not just the interpretation of history, but history itself.

Can you help me here?

 

[JesseM]

But let's say that just before the idlers get to the junction (in which they get "which-path"-ed, or erased) you decide to detect them all - that way you'll be able to tell between the interference pattern and the two lines - because they all were "which-path"ed!
In other words, if you detect all the idler photons' which path, then there shouldn't be any interference pattern!

By this reasoning, you could clearly discern whether there is an interference pattern or just two solid lines on the screen. And, if you can do this (at least till you can show me why my reasoning is flawed) you have the ability to change not just the interpretation of history, but history itself.

Can you help me here?

As I've already said, you never see an interference pattern in the total set of signal photons on the screen in this experiment, so doing what you describe won't cause you to see anything different on the screen than if you erased all the idler photons' which-path information. It's only after you've correlated the signal photons with the detector their idler went to that you may or may not see an interference pattern in subsets of signal photons whose idler went to a particular detector, depending on whether or not that detector is a which-path erasing one (in which case the subset shows interference) or a which-path preserving one (in which case the subset doesn't show interference).