I Delayed choice experiment clarification (specific setup)

I know that clarifications about delayed choice experiment was asked million times, and I understand the idea, but I was not able to find the discussion of this particular situation anywhere, though I tried hard. This setup is described in Brian Greene's Fabric of the Cosmos book (note my question is about modification of this setup, not about it exactly as described in book). Here is a picture of setup from the book

o1nad.jpg

So photon goes from source to the beam splitter, then there are two down-converters that split photon into two, each of which goes in different directions: one follows the previous path (that one is named "signal") and the other goes into different direction to the detector ("idler" photon). Two signal photons then go to detector. Without down-converters we see interference pattern in detector - that seems clear. With down-converters it is claimed that we don't see interference pattern because detecting idler photons reveals information about which path photon has "chosen": if photon detected in top detector - photon has chosen top path, if not - then bottom one. So interference pattern disappears (so is claimed in the book).

Then book follows to description of modification of this setup to erase which path information - this part is clear for me and it's not what I'm interested about. What is not clear is:

What if we remove idle photon detectors from the setup, but leave down-converters in place? Then it seems "which path" information is not revealed and interference pattern should appear again? But that does not make much sense, because we can decide to put or not a detector at much later time (after corresponding singal photon hit the screen). So depending on if we see pattern or not we should know what happened in the future, which of course cannot happen. Is that assumption about removing idler detectors leads to interference pattern incorrect? If so, why? What will happen if we switch idler detectors on and off by our choice?
 

Simon Bridge

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I know that clarifications about delayed choice experiment was asked million times, and I understand the idea, but I was not able to find the discussion of this particular situation anywhere, though I tried hard. This setup is described in Brian Greene's Fabric of the Cosmos book (note my question is about modification of this setup, not about it exactly as described in book). Here is a picture of setup from the book [deleted]

So photon goes from source to the beam splitter, then there are two down-converters that split photon into two,
... a down converter is a black box that takes a single photon as input and produces a pair of photons as output.
The input photon gets absorbed in a crystal inside the box - the output photons have a special relationship to each other and to the input photon.
The resulting output are usually entangled for eg. In the quantum eraser experiment, it is important that they are entangled.
It is not useful to think of it as just "splitting the photon".

Note: (for others googling here later) the experiment is run on one photon at a time, and the interference pattern is built up over a large number of runs.

...each of which goes in different directions: one follows the previous path (that one is named "signal") and the other goes into different direction to the detector ("idler" photon). Two signal photons then go to detector. Without down-converters we see interference pattern in detector - that seems clear. With down-converters it is claimed that we don't see interference pattern because detecting idler photons reveals information about which path photon has "chosen": if photon detected in top detector - photon has chosen top path, if not - then bottom one. So interference pattern disappears (so is claimed in the book).

Then book follows to description of modification of this setup to erase which-path information...
Greene starts out describing a Wheeler delayed choice experiment, and then proceeds to the quantum erasor experiment. OK.

- this part is clear for me and it's not what I'm interested about. What is not clear is:

What if we remove idle photon detectors from the setup, but leave down-converters in place? Then it seems "which path" information is not revealed and interference pattern should appear again? But that does not make much sense, because we can decide to put or not a detector at much later time (after corresponding signal photon hit the screen). So depending on if we see pattern or not we should know what happened in the future, which of course cannot happen. Is that assumption about removing idler detectors leads to interference pattern incorrect? If so, why? What will happen if we switch idler detectors on and off by our choice?
The entanglement introduced by the down-conversion means that interacting with the idle photon determines the state of it's signal photon.
Off Kim et al. (2000) original paper... iirc they tried that (left the detector switched off, but with the down converter in place, in some runs).
You have to have detected the idle photon to get the result. No detector, no detection. ie. I don't recall that the down-converter did the marking exactly.
The details are all about the properties of intangled pairs.

What is your education level?
 
... a down converter is a black box that takes a single photon as input and produces a pair of photons as output.
The input photon gets absorbed in a crystal inside the box - the output photons have a special relationship to each other and to the input photon.
The resulting output are usually entangled for eg. In the quantum eraser experiment, it is important that they are entangled.
It is not useful to think of it as just "splitting the photon".

Note: (for others googling here later) the experiment is run on one photon at a time, and the interference pattern is built up over a large number of runs.

Greene starts out describing a Wheeler delayed choice experiment, and then proceeds to the quantum erasor experiment. OK.

The entanglement introduced by the down-conversion means that interacting with the idle photon determines the state of it's signal photon.
Off Kim et al. (2000) original paper... iirc they tried that (left the detector switched off, but with the down converter in place, in some runs).
You have to have detected the idle photon to get the result. No detector, no detection. ie. I don't recall that the down-converter did the marking exactly.
The details are all about the properties of intangled pairs.

What is your education level?
Thanks for your reply. I have masters degree in computer science, but as for physics - Im a regular layman. Though I did take some efforts to understand quantum mecanics, so I understand the basics, or at least I think so. Yes I absolutely understand that down converter produces entangled photons, and what that means. My question is: without down converters we see interference pattern (right?). With down converters but without detectors, what do we see on the screen? I assume what we see can not be related to whether we measure idler photons or not (assuming of course that path made by idler photons are longer than signal photons). So I assume we see no interference pattern, whether we measure idlers or not. Is this assumption correct? If yes, then why exactly introducing down converters destroy interference? Because now we have two signal photons instead of one, and they have different phases?
 

DrChinese

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...assuming of course that path made by idler photons are longer than signal photons..
The ordering of detection is always irrelevant for signal and idler photons.

Many quantum phenomena display unusual time ordering characteristics. The Delayed Choice experiment you describe is one such. In fact, it is possible to entangle photons AFTER they have been detected. This may seem counter-intuitive (even impossible), but it is true. (Note: details of such do not allow you to send a message from the future to the past.)
 
The ordering of detection is always irrelevant for signal and idler photons.
Well, maybe I should not have put this comment. My main interest in this experiment is: do idler photon detectors play any role at all? If we remove them, switch them off, put them at different distances, or do anything else with them - will that change the overall distribution of signal photons (assuming down-converters are still in place)? Will we ever see an interference pattern as we did before we put down converters there?
 

DrChinese

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Well, maybe I should not have put this comment. My main interest in this experiment is: do idler photon detectors play any role at all? If we remove them, switch them off, put them at different distances, or do anything else with them - will that change the overall distribution of signal photons (assuming down-converters are still in place)? Will we ever see an interference pattern as we did before we put down converters there?
These types of delayed choice setups are notoriously difficult to talk about, as everything is very sensitive to the precise details of the setup. So what I am telling you may appear a bit confusing. However, in your modified version: photons that emerge from down conversion are not coherent*. Therefore the signal photons do NOT provide double slit interference. However, a subset of those will display enough coherence to provide double slit interference. Those that have sufficient coherence can be determined by a review of some attributes of the idler photons. In the delayed choice, that is usually done by registering in a focal lens. Idlers that register indicate that the matching signal photon will show interference (more or less, they are coherent). However, I would be hard pressed to say that registering the idler "causes" the signal to self-interfere. Again, my description is somewhat simplified, and may not suit everyone's fancy. You almost need to look at a number of these experimental setups before the basic ideas really emerge. So here are a couple of references that may help you:

https://arxiv.org/abs/1407.2930
Delayed-choice gedanken experiments and their realizations

https://arxiv.org/abs/1209.4191
Entanglement of photons that have never co-existed - this helps see some of the time ordering issues. There is no sense in which the idler affects the signal more than the signal affects the idler. Normal causal order is absent in many quantum contexts.

*Coherent in this situation more or less means: the photons have a specific position from which they started. Entangled photons are created within a crystal and do not have a specific point of origin. They act as if they have multiple points of origin. As a result, the interference between the different origin points (since there isn't just one) is destructive (they aren't in phase) and effectively disappears. This is a simplification, and probably an over-simplification at that. Coherent photons, on the other hand, have an origin point (or points) such that there is NOT destructive interference between paths (in phase). As a result, there IS interference on a double slit screen setup.
 

Strilanc

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In fact, it is possible to entangle photons AFTER they have been detected. This may seem counter-intuitive (even impossible), but it is true. (Note: details of such do not allow you to send a message from the future to the past.)
The "after the fact entanglement" stuff is always just correlations and postselection framed in a way that makes them sound spookier than they really are.

The experiments are described as if the future qubit measurements are determining the past qubit measurements. The "less spooky" framing is that the initial qubit measurements tell you the state of the remaining qubits, the new state depends on the measurement in counter-intuitive ways due to the entanglement, and the new state determines the later measurements.
 
These types of delayed choice setups are notoriously difficult to talk about, as everything is very sensitive to the precise details of the setup. So what I am telling you may appear a bit confusing. However, in your modified version: photons that emerge from down conversion are not coherent*. Therefore the signal photons do NOT provide double slit interference.
That was the missing piece in my puzzle. I've also read both references you mentioned, which certainly improved my understanding of this kind of experiments. Thanks for your help!
 

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