Question about delayed choice quantum eraser

[sunjen]

I was reading about the Delayed Choice Quantum Eraser experiment here:

bottomlayer.com/bottom/kim-scully/kim-scully-web.htm

In this experiment the which-path info is erased or not at random AFTER the original (signal) photon hits the screen. The results of the screen are seen by the experimenter AFTER the choice to erase or not took place.

I wonder what happens If the experimenter looks at the screen after the photons hit the screen but BEFORE the choice to erase the which-path is made? That is to have the idler photons still traveling and not reach yet the mirror that has a 50-50 chance of erasing the info.

Any ideas?

[Hurkyl]

If you're describing what I think you're describing....


One of the main points (which, IMHO, is woefully underemphasized in popular accounts) is that the screen always looks 'normal'. The interference pattern only appears in post-processing, after you've separated the images on the screen into two sets based upon what the other detector saw. (And, of course, only appears if you retained the which-path info)

[Demystifier]

Whenever I have conceptual doubts about delayed choice and quantum eraser questions, I use a trick: I first analyze what would be the answer in the Bohmian interpretation. Then I simply apply the theorem that states that measurable predictions of the Bohmian interpretation are identical to those of the standard interpretation. The advantage of this trick is that, even if you do not favor the Bohmian interpretation, this approach is conceptually simpler in the sense that it does not involve the wave-function collapse.

To see in more detail how the Bohmian interpretation works for delayed choice, see:
D. Bohm, C. Dewdney, B.J. Hiley, Nature 315 (1985) 294-297.

[vanesch]

Whenever I have conceptual doubts about delayed choice and quantum eraser questions, I use a trick: I first analyze what would be the answer in the Bohmian interpretation. Then I simply apply the theorem that states that measurable predictions of the Bohmian interpretation are identical to those of the standard interpretation. The advantage of this trick is that, even if you do not favor the Bohmian interpretation, this approach is conceptually simpler in the sense that it does not involve the wave-function collapse.


I do exactly the same thing with MWI :smile:
It is my main - if not sole - justification for considering MWI.

In fact, the reason why as well Bohm as MWI give clear answers in this kind of cases, is that they don't have a "measurement ambiguity" built in their formalism, but have a universal dynamics. In other words, you can "close your eyes and think of England" and let the formalism crunch the numbers - while in every projection-based viewpoint, you have to decide when you project and when you don't, and that's the difficulty here.

[sunjen]

Thanks guys for the response.

... the screen always looks 'normal'. The interference pattern only appears in post-processing, after you've separated the images on the screen into two sets based upon what the other detector saw. (And, of course, only appears if you retained the which-path info)

Ok So let's see these 2 scenarios

1) I look at the screen AFTER completely erasing the which-path info of all photons.
I see the interference pattern. right?

2) I look at the screen BEFORE completely erasing the which-path info of all photons. The idler photons have not reached the detectors yet.
You say I see the the normal distribution. right?
So in this case it doesn't make a difference if I see or erase the which-path info, I already saw the normal dist. and that won't change. right?

[atyy]

Quantum Erasure: Quantum Interference Revisited
Stephen P. Walborn, Marcelo O. Terra Cunha, Sebastião Pádua, Carlos H. Monken
http://arxiv.org/abs/quant-ph/0503073

"Wait Bob, that wasn’t there before! How did you make the photons interfere after I already detected them and recorded it all in my lab book?!”

[sunjen]

Thanks. I just read the article, very good by the way.

So what I understand is that if you have any means to measure the which-path information (even if not measured yet), and you see the screen you will see the normal dist. If afterwards you erase the info from a subset of the photons, you can see interference only in that subset.

But what about if you erase the info on all photons?

[Autochthon]

Good article think I'll send it to a few non QM literate friends. Every time I read about Quantum Erasure I'm left with this odd niggling feeling that I'm peering through this strange lens called "entanglement" and that as I examine an object through the lens I can't decide if I'm changing my focus and thus seeing the a different aspect of the object or the object itself is changing.

[Cthugha]

So what I understand is that if you have any means to measure the which-path information (even if not measured yet), and you see the screen you will see the normal dist. If afterwards you erase the info from a subset of the photons, you can see interference only in that subset.

But what about if you erase the info on all photons?

If you look at the paper you linked in your first post, you will notice, that there are two subsets - or joint detection rates - which can show interference if you destroy which-way information (Fig. 3 and 4). If you take a close look, you will notice that they are out of phase.

If you erase which-way info on all photons and just look at the screen without choosing a subset by doing coincidence counting, you will now see both of these interference patterns superposed, which will again be a normal distribution as they are out of phase. So there is still no interference pattern without doing coincidence counting.

[sunjen]

Thanks for the response!

So there is still no interference pattern without doing coincidence counting.

Now this raises another question:

In this experiment there is no interference without doing coincidence counting, but in the original double slit experiments the interference pattern is shown.

So why is that, what is the difference between the two?

[Demystifier]

Now this raises another question:

In this experiment there is no interference without doing coincidence counting, but in the original double slit experiments the interference pattern is shown.

So why is that, what is the difference between the two?
An analogy from everyday life may also be helpfull:
http://www.physicsforums.com/blog.php?b=7

[Cthugha]

In this experiment there is no interference without doing coincidence counting, but in the original double slit experiments the interference pattern is shown.

So why is that, what is the difference between the two?

Well the key to interference phenomena is indistinguishability of some sort. Comparing the simple double slit to quantum eraser experiments, you will notice, that we are talking about two different kinds of indistinguishability here.

The usual double slit uses the fact, that there is a fixed phase relationship of the incident light at both slits. If the phases at both slits were completely independent of each other, this would be some kind of which way information and the interference pattern would disappear. In order to avoid this, you need light, which is at least a bit coherent: The coherence length needs to be at least as large as the slit separation is. The light, which comes out of a BBO crystal used for spontaneous parametric down converion is rather incoherent. However one can increase the coherence length by putting the BBO crystal far away from the double slit. This equals choosing a small subset of wave vectors (or equivalently emission angles), which actually make it to the double slit, so the phase relationship at the double slit is better defined.

Quantum erasers and the like use indistinguishability of two-photon amplitudes. In this case the phase relationship of the two-photon state is well defined as the wave vectors of the two photons are correlated due to conservation of momentum. The detector D0 is positioned in the focal plane, so that each point inside the focal plane corresponds to exactly one wave vector. If the detector is small enough, this is a rather precise measurement of the photon wave vector.

Now the other entangled photon hits a double slit or some other kind of similar setup like in the paper you quoted. The light hitting this double slit is alone not coherent enough to show an interference pattern as there are plenty of different wave vectors arriving. However, if we detect a photon at the other detector, we measured the wave vector and therefore the wavevector of the other photon is pretty well defined due to conservation of momentum. So the subset of these joint detections has a clearly defined wave vector and therefore there will be some kind of interference effect in the coincidence counts.

However, to actually see an interference pattern in the coincidence counts at D0, you need a rather large spread of wave vectors, as every position in the plane corresponds to one certain wave vector. So the more wave vectors you include, the better will the visibility of your interference pattern be.

Now one sees that finding interference in the usual double slit needs a small spread in the wave vectors (which can be achieved by using a huge distance between light source and double slit) and finding interference effects in coincidence counting experiments needs a large spread in the wave vectors (which can be achieved by using a small distance between light source and double slit). As you can't have a small and a large distance simultaneously, both kinds of interference are complementary, so you can't have both at the same time with full visibility.