Question about spontaneous parametric down conversion

[Clovis]

I would like some help understanding some parts of spontaneous parametric down conversion (SPDC).In the Wikipedia article on the topic…http://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion…the third figure from the top is labeled “An SPDC scheme with the Type II output”. The figure shows two green cones coming out of a crystal. If I understand this figure, the top cone represents the range of possible locations for one of the two down converted photons (let’s say the top cone is the “signal” photon). The bottom cone represents the range of possible locations for the other of the two down converted photons (the “idler” photon). Both cones are shown with circular cross sections at their bottom.Here are my questions:1) In the Wikipedia article, it states that the two photons are “always symmetrically located within the two cones, relative to the pump beam.” Does this mean that if the signal photon is detected at the 12:00 position in the top cone, then the idler photon must be located at the 6:00 position in the bottom cone? And if the signal photon is detected at the 2:00 position in the top cone, then the idler photon must be located at the 8:00 position in the bottom cone?2) If it is true that detection of the signal photon at the 12:00 position in the top cone means that the idler photon must be located at the 6:00 position in the bottom cone, does that mean that the two photons are entangled? My understanding of the term “entangled” is this: Whenever a measurement of a property of one particle determines a property of another particle, the two particles are said to be entangled. It seems to me that the signal photon in the top cone can exist in a range of possible locations before we measure it, but if we measure it to definitely be at the 12:00 position, then we know that the idler photon in the bottom cone is definitely in the 6:00 position. In fact, from my limited understanding of quantum mechanics, I would say that our detecting the signal photon at 12:00 is what caused the idler photon to be located at the 6:00 position. That seems like entanglement to me.The reason I am asking the second question is that the Wikipedia article seems to say that the two photons are only entangled along the lines where the cones intersect. But (as I described above) I feel the two photons are entangled no matter where they are in their respective cones. Am I wrong in that?
Thank you,Clovis

 

[naima]

to 1) Yes
to 2)
the article says that some incoming photons are converted to correlated pairs. All these pairs are entangled. But entanglement is not synonimous with maximal entanglement.
with a maximall entanglement a result for one particle gives you the result for the other one measurement.
A looser entanglement will only give you an information for the second measurement which will enable you to win money if you are a gambler.

The article does not say that 06/12 photons are not entangled (they are) it says that 03/09 photons are entangled and "have perpendicular polarizations".

I come back to your idea about entanglement Suppose that you have two sources of paticles one gives you horizontal north moving particles. the other one is built to give you southwest moving particles. When you measure the momenum you always get perfectly correlated results. But they are obviously not entangled. You have entanglement when a part of the information is not in the particles but in their correlations.

 

[Clovis]

Thank you very much, Naima, for a very clear reply. It helped my understanding quite a bit.

I am pretty sure I understand the example you gave of non-entanglement in your last paragraph. I can see that if the particles come from two sources then they are not entangled. But if they come from the same source and are emitted at the same time, are they entangled?

 

[naima]

Let us stay in 1D
Take a particle which decays in two photons with a null total momentum.
If these photons are filtered so that they are H polarized, the pair system is described by the tensor product HH.
So it is NOT entangled
Bob will measure his polarization along another given direction, If Alice does the same and sends him the result the particles are said to be entangled if this increases BOB's probability to bet on the good result.
When a system is given by a tensor product of two pure states it is not entangled.

 

[DrChinese]

But if they come from the same source and are emitted at the same time, are they entangled?

They may or may not. Pairs from a *single* Type I PDC crystal are NOT polarization entangled. Input is H and output is VV. But I believe they are still momentum entangled. Interestingly, pairs from a suitably arranged *pair* of Type PDC I crystals ARE polarization entangled.

 

[Clovis]

Thank you both, Naima and Dr. Chinese. I think what I didn't understand before your responses is that there are sub-categories of entanglement. Particles can be entangled in some of their properties but not in others. For example, in the Wikipedia figure I referred to in my first posting, the photon pairs are momentum entangled anywhere in the cones, but only along the intersection of the two cones are they also polarization entangled. Is that it?

 

[naima]

I found the paper which was cited in wikipedia
http://people.bu.edu/alexserg/Entangled.pdf
I am going to read it.
Any comment?

 

[naima]

the photon pairs are momentum entangled anywhere in the cones, but only along the intersection of the two cones are they also polarization entangled. Is that it?

Do you think that they are only entangled on these two lines but if they are very near these lines entanglement disappears? There would be a physical dirac function on these lines?
I think that they are polarization EPR entangled on them and less polarization entangled in the neighborhood.