Understanding the Scully and Yoon-Ho Experiment: Interference in D0

[yuvalg1]

Hi,
I wanted to ask a question regarding the D0 detector in the original Scully and Yoon-Ho experiment (from 2000):

According to the paper itself, and to the wiki article:

"Note that 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.[3] 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[1]), 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 π phase shift between the two interference fringes"), so that the sum of the two will not show interference."

Now, suppose that the paths which the idler photons take are 1 light-year long, so that we can observe the pattern in D0 well before the idler photons are reach their detectors, and determine whether we'll find interference or not between them and their respective signal photons in D0.

Basically, my question is this -
From what I understand, all the photons that reached D0 have gone through a lense which erases their which-path data. So in a sense, if we only look at the path to D0, then we have a "regular" quantum eraser experiment!
In this case, why isn't there an interference pattern in D0?

Thanks in advance!

 

[Cthugha]

You will not see an interference pattern at D0 because the interference pattern in DCQE is a two-photon interference pattern which is a property of the biphoton state. That means that the two-photon state has some non-trivial joint coherence properties while each individual beam is incoherent and thus cannot produce interference pattern under the conditions used in DCQE experiments.

Such two-photon interference patterns are therefore visible only in coincidence counting and never visible at one detector alone.

 

[yuvalg1]

I see.
Thank you very much for the answer!

 

[yuvalg1]

Another clarification if you could, please -
According to the wiki article I cited, the reason for there not being an interference pattern has to do with the "∏ phase shift between the two interference fringes" (of R01 and R02 in the article).

According to what you say, the reason why there would never be an interference pattern in D0 alone, has nothing to do with that, right?

So is the reason supplied in the Wikipedia article incorrect?

 

[Cthugha]

The "∏ phase shift between the two interference fringes" is a somewhat reduced and boiled down explanation of what happens. These two patterns occur when the other detectors are placed at exactly one position each and coincidence counts with detections at this position are evaluated. However, the light field has some spread larger than the detector area and you would get slightly different patterns if you placed the other detectors elsewhere.

As the single beam is incoherent, you can also picture the pattern at D0 alone as the sum of all possible coincidence count interference patterns between D0 and the other detectors, placed at every possible position. Then you do not only get a sum over those two interference patterns with a phase shift of ∏, but also interference patterns corresponding to every possible position of the other detectors which has a different relative phase each. The sum over all of these phases gives no pattern at all.

 

[yuvalg1]

So the ∏ phase shift itself has to do with the different actual position of the detectors?
Placing the detectors otherwise would result in a different phase shift between the interference patterns fringes of the detectors (which had their which-paths erased), dependent on the relation between the idler photon and the specifc position/angle of the detector?

 

[Cthugha]

The pi phase shift results from the difference between transmission or reflection at the beam splitter. If you just trace one path through the beam splitter and place the detectors at the positions where the transmitted and reflected rays arrive, you will get a pi phase shift between them.

If you trace a different ray through the beam splitter and place the detectors at the new positions where these rays arrive, there will also be a phase shift of pi between them, but they will have a different phase offset compared to the first rays.

 

[yuvalg1]

I see.
However, this brings me back again to the original question:
According to the layout of the experiment the beam splitters affect only the idler photons. So, the signal photons, arriving through the lense at D0 supposedly shouldn't be affected until after the idler photons pass through the beam splitters and arrive at the other detectors.

If we make the path to the beam splitters and detectors 1-4 very long, why could we not look at D0 and see an interference pattern? What I mean is - you said that the setting of the DCQE uses a biphoton interference pattern. Is there a possibility to set up the experiment so that we would be able to check the interference pattern of the single photon (signal) at D0 and still be able to see the biphoton interference pattern it would have with the idler photon? If so, wouldn't we expect to always see an interference pattern in D0?

 

[Cthugha]

I see.
However, this brings me back again to the original question:
According to the layout of the experiment the beam splitters affect only the idler photons. So, the signal photons, arriving through the lense at D0 supposedly shouldn't be affected until after the idler photons pass through the beam splitters and arrive at the other detectors.

Correct, these photons are not at all effected by what happens on the other side.

If we make the path to the beam splitters and detectors 1-4 very long, why could we not look at D0 and see an interference pattern? What I mean is - you said that the setting of the DCQE uses a biphoton interference pattern. Is there a possibility to set up the experiment so that we would be able to check the interference pattern of the single photon (signal) at D0 and still be able to see the biphoton interference pattern it would have with the idler photon? If so, wouldn't we expect to always see an interference pattern in D0?

The prerequisites to see single-photon interference and two-photon interference are mutually exclusive. For single photon interference in a double slit you need spatial coherence corresponding to a small angular size of the source. For entanglement and two-photon interference you need a large angular size of the source. This is discussed in detail in A. F. Abouraddy et al., "Demonstration of the complementarity of one- and two-photon interference", Phys. Rev. A 63, 063803 (2001). This paper can also be found at the ArXiv.

 

[yuvalg1]

Very well.
Thanks again for all the clarifications!