Spontaneous parametric down conversion photons

[Dadface]

When I look at certain experiments involving entangled photons generated by spdc, for example quantum eraser experiments, it seems to me that each observed pair of entangled photons is propagated in a horizontal plane. However, aren't the entangled photons generated randomly in all planes, sometimes vertically as well as sometimes horizontally and at all angles between the vertical and horizontal? If so are all angles remote from the horizontal just eliminated from observations by virtue of the coincidence methods used. Or could it be that the system used to create the photons is prepared in such a way that the horizontal plane is the most likely?
Thanks for any replies.

 

[jfizzix]

Among other factors, the likelihood of SPDC is dependent on the degree of momentum and energy conservation, also known as phase matching.

Since the momentum of a photon depends on its wavelength; and the energy of a photon depends on its frequency; and the index of refraction changes with wavelength, there are only a few certain materials with the right optical properties, so that their indices of refraction will be just right at the correct frequencies to make both energy and momentum conservation possible.

Whatever the momentum of the input photon is, the momenta of each member of the output photon pair must add up to the momentum of the input photon.

Since the laser shining in a crystal cut for SPDC is shining in the horizontal direction, the momentum of the input photon is also going to be in the horizontal direction. The momenta of the two output photons must have horizontal components adding up to the momentum of the input photon, but they can have vertical components, so long as they are equal and opposite direction. In practice, the downconverted light will usually point out in different directions, but it will have a large component parallel to the momentum of the input photon.

 

[Dadface]

Thank you jfizzix. The point I'm trying to get at with this question is related to what is actually detected. It seems that in the experimental arrangements used the signal and idler detectors are in the same horizontal plane. If so then depending on the geometry of the system, including the effective face areas of the detectors, it seems that emergent photons with a vertical component of motion greater than a certain value will miss the detectors completely.

 

[DrChinese]

... this question is related to what is actually detected. It seems that in the experimental arrangements used the signal and idler detectors are in the same horizontal plane. If so then depending on the geometry of the system, including the effective face areas of the detectors, it seems that emergent photons with a vertical component of motion greater than a certain value will miss the detectors completely.

There are some setups where there is something of a plane. When PDC photons emerge, they are slightly off axis. Photons that go straight through are not down converted. The off axis ones are within relatively narrow angle bands. Let's say between 2.9 and 3.1 degrees is the sweet spot for finding entangled pairs. I believe the output beam is therefore essentially a cone. You can see much of this here, this has a single Type I crystal: http://departments.colgate.edu/physics/research/Photon/root/Apparatus/spdc.htm

Note that in the example, these are not polarization entangled pairs but they are entangled as to momentum. Also, I believe collection of photons is performed from a plane rather than a conic section. If I am correct, that means that most entangled pairs coming out of the crystal are not collected (as you were saying). On the other hand, there are other setups that operate differently, and I'm not sure of all the ways BBo crystals can be cut. But below shows clearly the conic shapes, and shows the setup with polarization entanglement using 2 Type I crystals. https://arxiv.org/abs/quant-ph/9810003

 

[vanhees71]

When I look at certain experiments involving entangled photons generated by spdc, for example quantum eraser experiments, it seems to me that each observed pair of entangled photons is propagated in a horizontal plane. However, aren't the entangled photons generated randomly in all planes, sometimes vertically as well as sometimes horizontally and at all angles between the vertical and horizontal? If so are all angles remote from the horizontal just eliminated from observations by virtue of the coincidence methods used. Or could it be that the system used to create the photons is prepared in such a way that the horizontal plane is the most likely?
Thanks for any replies.

What's pretty well determined is not the position of photons (photons do not have a position, strictly speaking, because they are massless quanta with spin 1>1/2) but the total momentum of the photon pair, which is given by the phase-matching condition, i.e., the total pair momentum and energy is given by the momentum and energy of the pump photon.

 

[Dadface]

Thank you DrChinese and thank you vanhees71. vanhees71 it is the observation of the photons that interests me at present