Double Slit Interference Question

[David Charles]

TL;DR Summary

I have a really straightforward (I think) question regarding the effect(s) of obtaining the which-path information of photons that have travelled through a double slit and are hitting a photosensitive screen. In the thought experiment, all the photons arriving at the screen have entangled twins which simultaneously arrive at which-path detectors that are either ON or OFF. The set up is super-simple but I can’t find this particular configuration - so not sure if it would actually work.

A laser provides a constant stream of photons which pass through a double-slit. The photon stream emerging from each slit then passes through a crystal which splits each photon into coherent entangled pairs. One photon from each pair heads towards a photosensitive screen and the entangled twin travels toward one of two detectors (one for the left slit, one for the right slit).

When the detectors are switched to the ON position, the which-path information for each photon (and its entangled twin) can be obtained. In this case, all photons behave as particles and do not interfere with one another. The pattern formed on the photosensitive screen does not exhibit a wave-interference pattern (no light and dark bands).

When the detectors are switched to the OFF position the which-path information for each photon (and its entangled twin) is completely lost. In this case, all photons behave as waves and interfere with one another. The pattern formed on the photosensitive screen exhibits light and dark bands (standard wave-interference pattern).

Question: Assuming 100% conversion of photons to entangled pairs, can an apparatus such as this be constructed/operate such that someone can, in real time, and only by observing the photosensitive screen, know whether the detectors are in the ON or OFF position? Thanks so much!

 

[Nugatory]

Assuming 100% conversion of photons to entangled pairs, can an apparatus such as this be constructed/operate such that someone can, in real time, and only by observing the photosensitive screen, know whether the detectors are in the ON or OFF position?

No.
But take a look at https://arxiv.org/pdf/quant-ph/9903047.pdf for a real experiment equivalent to what you’re describing here.

 

[David Charles]

Thanks so much, Nugatory - excellent article. I have a bunch of questions, if you can stick with me. I’ll start with two:

1) The article refers to “idler” and “signal” photons. Are these fundamentally different in any way, or is it just shorthand so we don’t have to say “the photon that reaches the interference screen” and “the photon that reaches the which-path detectors”?

2) My thought experiment uses a screen that you can just look at to observe the interference pattern but the the article refers to “detector D0, which can be scanned by a step motor along its x-axis for the observation of interference fringes”, so let’s use a detector like D0 for my system. What kind of graph (Fig 4 or Fig 5) would be generated if we removed the half-silvered mirrors, and let all the idler photons be detected by detectors that would definitely provide the which-path information for every single idler photon?

 

[mfb]

1) The article refers to “idler” and “signal” photons. Are these fundamentally different in any way, or is it just shorthand so we don’t have to say “the photon that reaches the interference screen” and “the photon that reaches the which-path detectors”?

They are just names to make clear which path is meant.

If you can recover the which-path-information you don't get an interference pattern.

 

[DrChinese]

Summary:: I have a really straightforward (I think) question regarding the effect(s) of obtaining the which-path information of photons that have traveled through a double slit and are hitting a photosensitive screen. In the thought experiment, all the photons arriving at the screen have entangled twins which simultaneously arrive at which-path detectors that are either ON or OFF. The set up is super-simple but I can’t find this particular configuration - so not sure if it would actually work.

A laser provides a constant stream of photons which pass through a double-slit. The photon stream emerging from each slit then passes through a crystal which splits each photon into coherent entangled pairs. One photon from each pair heads towards a photosensitive screen and the entangled twin travels toward one of two detectors (one for the left slit, one for the right slit).

When the detectors are switched to the ON position, the which-path information for each photon (and its entangled twin) can be obtained. In this case, all photons behave as particles and do not interfere with one another. The pattern formed on the photosensitive screen does not exhibit a wave-interference pattern (no light and dark bands).

When the detectors are switched to the OFF position the which-path information for each photon (and its entangled twin) is completely lost. In this case, all photons behave as waves and interfere with one another. The pattern formed on the photosensitive screen exhibits light and dark bands (standard wave-interference pattern).

Question: Assuming 100% conversion of photons to entangled pairs, can an apparatus such as this be constructed/operate such that someone can, in real time, and only by observing the photosensitive screen, know whether the detectors are in the ON or OFF position? Thanks so much!

There are a lot of issues with a setup such as you describe. They get quite complicated as you dig in. A few things to note:

1. It does not matter whether the detectors are ON or OFF. In no case will there be any kind of "erasure". To the world, the information on which detector would have been triggered exists anyway.

2. Generally, entangled photon pairs do NOT provide the kind of interference you imagine on the screen. Certainly there would need to be complete erasure before this could even be considered.

 

[David Charles]

Thanks, DrChinese. Let me ask a few questions to try to understand what's happening. Let's say we shoot a single photon, which travels through the double slit, and then is split into entangled twins. The detectors are ON and the idler twin is detected as either having come through the left or the right slit. From this, do we know that the signal photon will behave as a particle, and not a wave? And if we repeat the process, but place an object (like a piece of plywood) in front of the detectors, and thus lose all-which path information, do we know that the signal photon will behave as a wave?

 

[Nugatory]

From this, do we know that the signal photon will behave as a particle, and not a wave?

You have been misled by the old and largely abandoned idea of wave-particle duality, which is no part of the modern (later than 1930 or thereabouts) formulation of the theory. Unfortunately by then it had made it into the popular imagination where it lives on as a sort of urban legend, one of those things that “everyone knows” but isn’t so.

A photon doesn’t switch between behaving like a wave or a particle - it behaves like a photon always, and this behavior is unlike anything in our classical experience. When physicists first encountered this behavior early in the 20th century they tried to understand it in terms of waves and particles because those classical concepts were all they had to work with at the time, so came up with wave-particle duality.

So back to your question... When a photon interacts with matter, it delivers all of its energy and momentum in a single lump at a single place in space and time - a dot appears on a piece of photographic film, for example. In the double slit experiment, the photons are more likely to appear in some areas of the film and less likely to appear in others. The interference pattern builds up over time as more and more photons hit the film and create dots, with more of them in some areas than others.

The probability of a photon appearing at any given point on the screen is calculated from all the possible paths the photon might have taken; if paths through both slits are possible their contributions to the probability will add at some points and cancel at others, leading to the interference pattern,

However, a path is only possible in the context of the entire experiment. if we block one of the slits then paths through that slit are no longer possible and they do not contribute to the probability. With your hypothetical piece of plywood, we have to ask where on the plywood the idler was absorbed; that in turn determines which paths are possible throughout the entire experiment.

Feynman’s book “QED: The strange theory of light and matter” is a good layman-friendly description of this idea of summing contributions from all possible paths.

 

[David Charles]

Thanks, Nugatory - yes, I guess I'm not precise in my terminology and employing old school ideas. (and I have read QED - fascinating).

So let me rephrase my question and feel free to rewrite it yourself if you can get where I'm leading.

My question is basically this: if we send a single photon through a double slit and it subsequently reaches a crystal which splits it into signal/idler twins, if we obtain the which path information for the idler (which alters the wave function for the idler?), does this action immediately alter the wave function for the signal photon?

 

[mfb]

There is no "wave function for the signal photon". You can't split the wave function into components, you need to consider the full wave function of the system (that's the point of entanglement).

 

[PeroK]

My question is basically this: if we send a single photon through a double slit and it subsequently reaches a crystal which splits it into signal/idler twins, if we obtain the which path information for the idler (which alters the wave function for the idler?), does this action immediately alter the wave function for the signal photon?

If two particles are entangled, they don't have separate wave-functions. There is a single wave-function for the two-particle state. That's the main point. There is no "wave function for the idler", for example.

 

[DrChinese]

Thanks, DrChinese. Let me ask a few questions to try to understand what's happening. Let's say we shoot a single photon, which travels through the double slit, and then is split into entangled twins. The detectors are ON and the idler twin is detected as either having come through the left or the right slit. From this, do we know that the signal photon will behave as a particle, and not a wave? And if we repeat the process, but place an object (like a piece of plywood) in front of the detectors, and thus lose all-which path information, do we know that the signal photon will behave as a wave?

A measurement indicating which path on one will give you similar information on the other. There would be no interference pattern of course.

As already mentioned by Nugatory and others, the particle wave duality terminology has been abandoned in most recent treatments, and is used as shorthand when exactness is not important. It would be more accurate to say that a photon (or group thereof) can be made to act as 100% particle, 100% wave, or any mixture in between. But again this is strictly determined by the total context of an experiment. This is especially true with erasure and entanglement experiments.

 

[David Charles]

Thanks, so much Dr. Chinese and everyone. I'm intrigued that the "particle wave duality terminology has been abandoned". I'm interested in learning more about this. I've posted a similar question with new figures that I hope can help me understand this behavior. See "Double Slit Interference Question II". I'm abandoning this thread because I didn't want to continue with the figure I used in this post.

 

[bhobba]

You have been misled by the old and largely abandoned idea of wave-particle duality, which is no part of the modern (later than 1930 or thereabouts) formulation of the theory.

Indeed. But to the OP please understand that in physics, especially QM, during the early stages of studying it outdated ideas like wave particle duality are often used. Even well respected teachers like Feynman recognised it and tried as much as possible to avoid it, but found it was not really possible. It's an issue that needs always to be in the back of peoples minds when they study QM. I have read this thread and just as another example it was mentioned 'if we send a single photon through a double slit'. Unless you actually measure it, which will change the experiment, how do you know it went through the slits? Feynman used the words 'in some sense going through both slits' to try and be carefull. But people often do not notice the subtlety here. See what I mean that it is really hard at the start to be 'exact' in understanding what is happening. Most people, including myself, develop a more nuanced view as they learn more. Realising this from the start will help a lot in keeping issues clear in your mind. I fell for exactly the same traps when I first started, and I had read advanced texts like Ballentine. It was only since coming here things became clearer over time. I used to think, for example, that QM objects were in different places at the same time, and some books even say that, but it is wrong - again unless you measure it you can't really say anything.

Thanks
Bill

 

[bhobba]

Thanks, so much Dr. Chinese and everyone. I'm intrigued that the "particle wave duality terminology has been abandoned". I'm interested in learning more about this.

The history is, from the wave-particle duality idea, Schrodinger's wave mechanics was developed. But there were other theories, just as good, also around - namely Matrix Mechanics of Heisenberg, and the lesser known q numbers of Dirac. It was suspected they were pointing to a more general theory, so the hunt was on.

It happened when Dirac (and independently Jordan - but Dirac is the one it's usually associated with) published his paper in early 1927 (but developed late 1926) on what is called transformation theory, which generally goes by the name QM these days:
https://arxiv.org/pdf/1006.4610.pdf

That focused on the concept of 'state' rather than waves etc. 'Waves' were still part of the new theory, but was just one way of expressing a state and they were not like the usual concept of a wave here in the classical world. So it's not a concept used except at the beginning level these days.

Thanks
Bill

 

[David Charles]

Thanks so much, Bill.

Could you take a look at my follow-up post here?:

https://www.physicsforums.com/threads/double-slit-interference-question-ii.990311/

I’m trying to drill down to what we would measure by a simple apparatus. Maybe you could either answer my question or help me ask the right question.

 

[phinds]

@David Charles something I find helpful to avoid the whole issue of "wave particle duality" is to realize that photons and other quantum objects are just that --- quantum objects. They aren't really waves or particles they are quantum objects. If you measure a quantum object for particle-like characteristics, you get them and if you measure it for wave-like characteristics you get them but that does not make it a particle or a wave.

 

[David Charles]

@David Charles something I find helpful to avoid the whole issue of "wave particle duality" is to realize that photons and other quantum objects are just that --- quantum objects. They aren't really waves or particles they are quantum objects. If you measure a quantum object for particle-like characteristics, you get them and if you measure it for wave-like characteristics you get them but that does not make it a particle or a wave.

Thanks, I like that.

If you have time, could you take a look at my follow-up post here:

https://www.physicsforums.com/threads/double-slit-interference-question-ii.990311/

I'm trying to see if a simplified apparatus will destroy an interference pattern. I have several other questions, but I'm trying to go one question at a time. Not sure if I'm asking the question correctly. Maybe you can help.

 

[phinds]

I'm trying to see if a simplified apparatus will destroy an interference pattern. I have several other questions, but I'm trying to go one question at a time. Not sure if I'm asking the question correctly. Maybe you can help.

'fraid not. I don't go that deeply into those things.

 

[bhobba]

I’m trying to drill down to what we would measure by a simple apparatus. Maybe you could either answer my question or help me ask the right question.

I am a mathematician with an interest in QM which unfortunately means I am not that well acquainted with the experimental aspects of it. I had a quick look and couldn't disentangle the experiment so will have to leave it to others more at home with that sort of thing. But I can point you to a reference, that within a particular interpretation, Consistent Histories (also called Decoherent Histories), explains how such are resolved:
http://quantum.phys.cmu.edu/CHS/histories.html

As an aside it is the interpretation Feynman was converted to just before he died. It happened after his colleague in the room next door where he worked at Caltech, Murray Gell-Mann, gave a talk on it and Feynman attended. Feynman sat quietly at the back of the room, and at the end got up. Everyone thought it was going to be a ding dong between titans - but instead he said - I agree with everything you said - and walked out. It's not necessarily the interpretation I hold to, but I do like it, and there is a lot of literature on how it solves experimental 'conundrums'.

Thanks
Bill

 

[Cthugha]

I'm trying to see if a simplified apparatus will destroy an interference pattern. I have several other questions, but I'm trying to go one question at a time. Not sure if I'm asking the question correctly. Maybe you can help.

This is not how the DCQE works. You do not "destroy" the interference pattern. The light arriving at the moving detector is incoherent. There is no interference pattern to start with. What is happening is that by using coincidence counting you can sort the full set of detections into two sets of interference patterns that are out of phase with each other (and sum up to the no-interference pattern). This sorting is only possible if you have no which-way information because otherwise the two detectors can not be mapped 1:1 to the two interference patterns.

So, no, you do not destroy the interference pattern. One rather restores it by filtering the results. In other words, one rather takes the stonemason's approach and removes detection events until the leftover forms an interference pattern. Accordingly, the answer to every single experimental variation of the DCQE experiment that uses entangled light, but does not use coincidence counting, is the same: there will be no interference pattern.