Some questions about Wheeler's delayed choice experiment

[liuxinhua]

TL;DR Summary

The problem of Wheeler's delay erasure experiment results，based on Wheeler's delay choice experiment.

Based on Wheeler's delay choice experiment, the following results of experiment1 can be achieved.

Experiment 1, the light passed through the BS1, 50% of the light is transmitted on optical path A, and then passed through the polarizer P2(the polarization angle is 135°),and the polarizer P3 (the polarization angle is 90°), then the light of light path A converges with the light of light path B at BS2;On the optical path B, the polarization angle of the polarizer P1 is 45°, the polarization angle of the polarizer P4 is 90°.
Through the BS2, the light is divided into two directions, one part goes to the detector D1, the other part goes to the detector D2, and the optical path is adjusted to make the light coherent in the D1 direction, and the light intensity in the D2 direction is cancelled.

Using a fixed frequency normal light source instead of a single photon light source, the light intensity can be measured on the detector.
Assume the light intensity of source light is 4 unit. Then the light intensity after the polarizer P1 is the same as that after the polarizer P2, which is 1 unit.
Adjust the optical path to make the light coherent in D1 direction, the light intensity at D1 position is 1 unit, and the light intensity cancellation at D2 position is 0 unit.

Experiment 2: on the basis of experiment 1, the polarizer P3 was moved to the position between the BS2 and the detector D1; the polarizer P4 was moved to the position between the BS2 and the detector D2.

Whether the result is the same as the experiment 1, the light intensity at D1 is 1 unit, and the light intensity at D2 is 0 unit.

It seems that the experiment 3: Remove P2 and adjust the polarization angle of polarizer P3 P4 to be the same as that of P1 based on Experiment 2, was actually realized.
But I didn't find the relevant literature.
Experiment 3:

Set the intensity of light source be 4 units. The polarizers P1, P5 and P6 have the same polarization angle (the same polarization angle45°).
The coherence of light intensity at D1 is 2.5 units, and that at D2 is 0.5 units.

What I want you to help me with is：
Is the result of Experiment 2 correct?
Is Experiment 3 implemented and where is the original literature?

 

[Strilanc]

You can try all of these in a simulator and see what it says: https://lab.quantumflytrap.com/

For example, here's my quick attempt at your setup #1:

I think this simulator negates the amplitude of one of the polarizations when the light bounces off a mirror or beam splitter. You might have to adjust for those sorts of minor differences in how exactly things are modeled.

 

[Jarek 31]

The above seem just variations on Mach-Zechnder, Wheeler experiment requires something more: https://en.wikipedia.org/wiki/Wheeler's_delayed-choice_experiment

The original one concerns looking at double-slits from a distance, e.g. imagine that photons could go from the left or right side of a planet.
If our telescope is able to distinguish these two cases, we should get classical statistics.
If it isn't, we should get interference.
It brings a question if photons travel through one (classical view) or both (quantum) trajectories - we can choose one of them by choice of observation method ... so what if various observers use different ways?

The 2006 successful experimental realization by Aspect's group ( https://arxiv.org/pdf/quant-ph/0610241 ) has indeed used Mach-Zehnder, but the key is lifting or not the final beamsplitter.
If it is lifted, we have classical view: photon travels one trajectory.
Otherwise, we have interference - photon travels both paths.
The problem is that they managed to choose to lift or not after the photon has passed the first beamsplitter - after the "choice of one or two trajectories" was made:

Naively it requires retrocausality ... unless we assume that always there is something traveling both trajectories - corpuscle through one, pilot/theta wave through second path.
From http://redshift.vif.com/JournalFiles/V16NO2PDF/V16N2CRO.pdf :

 

[PeterDonis]

after the photon has passed the first beamsplitter - after the "choice of one or two trajectories" was made

Why would passing the first beam splitter make the "choice of one or two trajectories"? All passing the first beamsplitter does is split the photon's wave function into two spatially separated parts. It doesn't "commit" the photon to traveling on either just one part or both of them.

The only "choice" that actually gets made anywhere is when the detectors D1 or D2 register a photon.

 

[Jarek 31]

The standard interpretation is: classically photon travels one path, for interference it needs to travel both simultaneously.
These two scenarios start differing at the first beamsplitter (BS_input), while being chosen by lifting or not the second (BS_output) - see e.g. Aspect's https://science.sciencemag.org/content/315/5814/966

Assuming there is a difference between these two scenarios, it can be "chosen delayed", also if you say that this choice was made by registering by D1 or D2.

 

[PeterDonis]

The standard interpretation is: classically photon travels one path, for interference it needs to travel both simultaneously.

No, the "standard interpretation", meaning the minimal interpretation of QM that is the one to be used for discussions in this forum (as opposed to the QM interpretations forum), is that there is no "path" for the photon at all unless you measure it. Since you're not measuring where the photon goes in this experiment until either detector D1 or detector D2 registers a photon, the only thing you can say about where the photon goes is that it hit the detector that registered.

If you have a reference to a particular QM interpretation that claims that "classically the photon travels one path, for interference it needs to travel both simultaneously", you can start a separate thread in the interpretations forum if you want to discuss it.

 

[PeterDonis]

if you say that this choice was made by registering by D1 or D2.

Registering D2 doesn't actually tell you anything for a single run, since (assuming the usual orientations of the beam splitters, i.e., the second beam splitter will always output the photon in the same direction as the incoming photon came into the first beam splitter), D2 could register whether the second beam splitter was there or not; if the second beam splitter is there, D2 will fire on every run, but if it isn't there, D2 will still fire on 50% of the runs.

Registering D1 would indeed only be possible if the second beam splitter was absent. But if D1 registers in a particular run, you can't change that by putting the second beam splitter back in after it registers. So there is no "retrocausality" required at all. Choosing whether or not to put the second beam splitter back in before any detector has registered is of course possible, but doesn't imply any kind of "retrocausality", since, as noted in my previous post, the photon's path is not being measured so you cannot say that the beam splitter got put back in "after the photon passed".

 

[Jarek 31]

So what happens classically: when BS_output is lifted?

 

[PeterDonis]

what happens classically

We are not talking about classical physics, we are talking about QM. So asking "what happens classically" makes no sense.

If you mean, what does classical EM predict about this experiment, classical EM doesn't even have "photons" to begin with, so it can't explain why detectors D1 and D2 register discrete photons at all. So classical EM is simply a non-starter for analyzing experiments like this one.

 

[Jarek 31]

Ok, so photon reflecting from mirror changes momentum - both own and so of the mirror.

Which of the two mirrors should get this change of momentum?
Maybe both?

E.g. imagine everything happens in completely empty vacuum with zero initial velocities - which mirror will eventually fly away after sending single photon through such MZ interferometer?

 

[Cthugha]

Ok, so photon reflecting from mirror changes momentum - both own and so of the mirror.

Which of the two mirrors should get this change of momentum?
Maybe both?

E.g. imagine everything happens in completely empty vacuum with zero initial velocities - which mirror will eventually fly away after sending single photon through such MZ interferometer?

This depends on the mirror you use. If you use an extremely light mirror mounted on a spring or a cantilever, you may see the momentum transfer. In this case, there is no interference afterwards and you know the path the photon took.

For any standard realistic mirror, a quantum treatment still needs to take the initial uncertainty in position and momentum into account. The change in momentum introduced by photon reflection is tiny compared to the inherent momentum uncertainty, so the states of the mirror before and after the reflection of a photon will have an overlap of 99.99...% In other words: The mirror is not a good measuring device for the momentum transfer and it is in principle impossible to measure the photon path this way.

 

[Jarek 31]

So imagine it happens in empty vacuum - all the elements are floating disconnected, with zero initial velocity
Single photon should add velocity to one of mirrors - if waiting long enough before checking this setting, couldn't we conclude which mirror was it from displacement?

If so, should this possibility of conclusion destroy the interference?

Also, what about intermediate situations, like changing this time before checking - this way controlling displacement size?

Examples of such intermediate cases between classical and quantum are weak measurements, like "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" https://science.sciencemag.org/content/332/6034/1170.full

 

[liuxinhua]

Thanks for the simulation website provided by Strilanc.

The following two results are found: the input difference is that the angle of the first polarizer is different. The result is a coherent enhancement in D1 direction and another coherent enhancement in D2 direction.

 

[Cthugha]

So imagine it happens in empty vacuum - all the elements are floating disconnected, with zero initial velocity
Single photon should add velocity to one of mirrors - if waiting long enough before checking this setting, couldn't we conclude which mirror was it from displacement?

If so, should this possibility of conclusion destroy the interference?

Also, what about intermediate situations, like changing this time before checking - this way controlling displacement size?

Examples of such intermediate cases between classical and quantum are weak measurements, like "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" https://science.sciencemag.org/content/332/6034/1170.full

Again: In QM there is no zero initial velocity. There is momentum uncertainty. When preparing the floating mirror repeatedly, it will move away irrespectively of whether it was hit by a photon or not. The crucial question is whether the additional momentum introduced by the photon is enough to become stronger than the width of the intrinsic momentum distribution due to uncertainty. If it is, then you have a strong measurement and no interference. If not, you of course can get a weak measurement that tells you how much each of the momentum distributions are shifted by the presence of the photon. However, you do not get any information from that beyond the information how many photons took which path on average - so essentially you just remeasured the splitting ratio of the beam splitter. You do not learn anything about the path of any individual photon.

Accordingly, the waiting time is completely irrelevant for all practical purposes. It just increases the precision with which you can measure the momentum.

 

[Jarek 31]

Instead of being focused on subjective observer, shouldn't we focus on objective physics?
And objectively the photon during reflection transfers momentum to one or two mirrors, making such two scenarios objectively different.

But generally this is much more complex than these simplifications, like explanation from Feynman lectures of reflexion using interference of such EM waves.

I have just found 2017 paper: https://arxiv.org/abs/1709.10344 with such trial to understand Mach-Zehnder:

 

[PeterDonis]

objectively the photon during reflection transfers momentum to one or two mirrors

As has already been pointed out, this is only true if you are measuring the momentum change of the mirrors. (And there are severe limitations to such measurements, as @Cthugha has pointed out.) If you aren't making such measurements (or if you are trying to, but are unsuccessful because of all the limitations), you can't make any "objective" assertions about what happens at the mirrors.

 

[Cthugha]

Instead of being focused on subjective observer, shouldn't we focus on objective physics?
And objectively the photon during reflection transfers momentum to one or two mirrors, making such two scenarios objectively different.

It sounds a bit as though you are lacking the very basics of quantum mechanics. In that case it might make sense to take one step back and start with a good book on qm. Sakurai's book is great for those with solid prior knowledge on qm. Kroemer's book is quite nice for those on the other end of the spectrum.

I take it that you mean "distinguishable" by "different". And in that case the overlap between the state before and after the mirror was hit by a photon tells us whether these state are distinguishable or not. They may be distinguishable, as is commonly the case in e.g. cavity optomechanics, where one might mount extremely light mirrors on cantilevers or springs. In pretty much every other case the overlap is large and the scenarios are objectively NOT different and cannot be told apart by any means. It is quite a trivial exercise to calculate the momentum uncertainty of a solid mirror and compare the standard momentum exchanged by reflection of a photon to that value. You can do that yourself very easily.

But generally this is much more complex than these simplifications, like explanation from Feynman lectures of reflexion using interference of such EM waves.

I have just found 2017 paper: https://arxiv.org/abs/1709.10344 with such trial to understand Mach-Zehnder:

That paper is utter nonsense. For example: "the presence of media is a necessary condition for interference of single photons, a photon interferes with other photon via microscopic particles in the interface of media". That is just plain wrong. If this was correct, one would have to perform the double slit experiment on interfaces.

 

[liuxinhua]

Does the vertically polarized light become horizontally polarized after reflection?

You can try all of these in a simulator and see what it says: https://lab.quantumflytrap.com/

For example, here's my quick attempt at your setup #1:

View attachment 282212

I think this simulator negates the amplitude of one of the polarizations when the light bounces off a mirror or beam splitter. You might have to adjust for those sorts of minor differences in how exactly things are modeled.

 

[liuxinhua]

What is the difference between the two results?
Why is the light incoherent after passing through the BS2 in the second figure?