Is the Coincidence Counter Essential in Birgit Dopfer's Experiment?

[alexepascual]

This topic has been extensively discussed on this forum during the last few years, but I don't see much discussion on it lately.
So this is an invitation to renew the debate on the subject.
It seems to me that there are still open questions and I haven't seen a good analysis of it.
I personally think that Anton Zeilinger's explanation on his paper "Experiment and the foundations of quantum physics" does not answer all the questions and some of his statements may not be correct.
For those new to the topic, an introduction can be found in:
www.paulfriedlander.com/text/timetravel/experiment.htm
A common point of disagreement is if the coincidence counter plays any role besides eliminating photons that don't have an entangled partner. Some say that without the coincidence counter you could never see interference in principle even if all the "noise" was eliminated. I haven't seen a good explanation as to why this would be true.
John Cramer at the University of Washington had claimed he would run an experiment equivalent to Dopfer's but without a coincidence counter, which would enable sending messages "back in time". I don't think we have had any news about his experiment lately.

 

[Cthugha]

Some say that without the coincidence counter you could never see interference in principle even if all the "noise" was eliminated. I haven't seen a good explanation as to why this would be true.

This is because single-photon interference and two-photon interference are complementary. See "Demonstration of the complementarity of one- and two-photon interference" by A.F. Abouraddy et al., Phys. Rev. A 63, 063803 (2001).

In a nutshell you need first-order-coherent light to see a single photon interference pattern. You need entanglement (or at least correlations) to see a two-photon interference pattern. The requirement for first-order coherence is a small spread in the emission angles of the photons. The requirement for entanglement (by violations of the Bell inequality) is a large spread in emission angles. As these two conditions contradict, you cannot get both interference patterns with reasonable visibility at the same time as would be needed for a setup without coincidence counting. All of this is discussed in Dopfer's PhD thesis (unfortunately written in German).

By the way you can easily get a single photon interference pattern without coincidence counting by just increasing the distance between the PDC crystal and the double slit up to the point of destroying entanglement because the small spread of emission angles at the double slit position becomes insufficient to violate Bell inequalities. Although this even decreases the count rate and increases noise, you can see the single photon interference pattern directly which nullifies the argument that coincidence counting is needed to reduce noise. Dopfer showed that in her thesis, too.

 

[alexepascual]

Cthugha: I will read the article you mentioned. With respect to Dopfer's thesis, I do have a copy of it but even though I started translating with the assitance of Google translations and some other Web based tool, I just managed to translate a small fraction of it as I got busy with other things. I have read the whole Zeilinger article but as I mentioned I think his explanation is not satisfactory.
Thanks for your input and I'll let you know what I think after I read that article.