Young's double slit experiment: reconciling facts and theory

FJBallesteros

I've read in many places that if, in a Young's double slit experiment, you can determine by whatever method through which slit your photon goes through (enhancing the "particle" behavior of light), then the interference pattern dissapears.

For this reason Zeilinger says that entangled photons do not produce interference patterns (because one could always use one photon of the pair to determine through which slit the other photon goes through).

And related with this is the fact stated by Dirac that interference between different photons never occurs.

BUT:

a) A friend of me works at GSI with neutral pions. Neutral pions decay to two entangled photons going in opposite different directions. And she says that they work routinely with the interference of these photons.

b) In 1963, Mandel and Magyar published an experiment in Nature (doi:10.1038/198255a0) where they produced interference fringes using two independent laser beams. The exit window of every laser can be considered as a single slit, so you have a double slit experiment which produces an interference pattern, where you know perfectly through which slit every photon has passed.

How these facts reconcile with the above statements?

Cthugha

This is roughly correct.

This is a bit simplified. A more correct phrasing is that it is impossible to create a situation where photons show an interference pattern and maintain entanglement in a meaningful sense as measured by one of the typical inequalities.

This is not a fact. This is at best a strange take on what different photons are. Let me cite someone way more knowledgeable than me, Nobel prize winner Roy Glauber (from "Quantum Optics and Heavy Ion Physics", Nuclear Physics A Volume 774, 7 August 2006, Pages 3–13):

"When you read the first chapter of Dirac's famous textbook in quantum mechanics [8],
however, you are confronted with a very clear statement that rings in everyone's memory.
Dirac is talking about the intensity fringes in the Michelson interferometer, and he says,
Every photon then interferes only with itself. Interference between two different
photons never occurs. Now that simple statement, which has been treated as scripture, is absolute nonsense."

There is no problem with that. You can also get interference patterns from entangled photons. For example for momentum-entangled photons you will see interference if you use a small detector in the very far field. Basically that means you collect photons from a smaller solid angle which increases coherence. However, entanglement means that the sum of the momenta (or equivalently the sum of the angles relative to the pump beam) is constant for each photon pair, while the fluctuations of the individual photon momenta are large. Going to far-field conditions where an interference pattern is visible now means that you are not able to measure these fluctuations in the individual momenta anymore which means that entanglement becomes pretty meaningless.

A good discussion on that topic can be found in "Demonstration of the complementarity of one- and two-photon interference" by A. F. Abouraddy et al., Phys. Rev. A 63, 063803 (2001).

Do you? How exactly do you know from which maser a photon at the detection screen came? You need to be able at least in principle to backtrack from which slit some photon camein order have no interference pattern. Just having two slits at different positions is not enough.

DrChinese

Thanks for this reference! Here is the arxiv version:

http://arxiv.org/abs/nucl-th/0604021


This to FJBallesteros:

Welcome to PhysicsForums!

You can have interference but there will not be the kind of entanglement left to also get the perfect correlations you might otherwise expect.

FJBallesteros

Ok, I think almost everything is understood now.

Cthugha

Oh, I did not notice he is a new face.
Welcome to these forums!

Just to add on what I have written before, it is maybe a bit unfair to tackle Dirac's statement from the modern perspective like Glauber did. Dirac formulated it way before quantum optics came up and even many basic issues of qm were not understood properly in Dirac's time. Nevertheless the statement is so catchy that it routinely comes up again and again and often does more harm than good.

DrChinese

Yes, I have seen it many times. I thought it could not be correct, so I bookmarked the reference. Obviously Glauber is gold for something like this.