Is it possible for a BBO crystal to produce an interference pattern?

[Herbascious J]

TL;DR Summary

Is it possible under any circumstances for a BBO crystal placed after a double slit to produce an interference pattern?

This question originated under a separate thread (see below) in an attempt to better understand what is happening with the quantum eraser experiment. Specifically, it seems that the BBO crystal which splits the photon beam after the double slit is critical in how the experiment is setup.

Regarding the crystal, If a laser is directed at a BBO crystal, it is my understanding that the majority of photons will pass straight through the crystal. However, a small minority of photons will under go "spontaneous down-conversion", meaning that a single photon will split into two, less energetic photons, that are identical and entangled. These two photons will be emitted from the crytsal at angles moving away from each other in specific directions. The assumption is that these photons will each have exactly half the energy of the parent photon and therefore have exactly double the wavelength. It is these two entangled split beams of light which are the subject of the quantum eraser experiment. This question is only about the behavior of the BBO crystal. The question is as follows...

Imagine a laser passes through a double-slit, immediately after which a BBO crystal is placed. Two entangled beams of light emit out at angles from the crystal. Each of these beams of light have light coming from both slits. Each beam is directed onto a simple screen so the light and it's pattern can be displayed, the assumption being, each screen shows an identical pattern, one a copy of the other. Keep in mind no which way information is known anywhere in the equipment. Do the screens show interference? Are there any circumstances where the BBO crystal can emmit light that shows an interference pattern that is preserved? What assumptions in this thought experiment are possibly misleading (eg. the beams may not be exactly double the wavelength of the parent beam in a discreet way).

https://www.physicsforums.com/threa...ff-sensor-to-bring-back-interference.1055858/

 

[vanhees71]

I think the single photons in the pair can show interference patterns, as confirmed, e.g., in the paper by Walborn et al on their realization of the delayed choice quantum eraser:

https://arxiv.org/abs/quant-ph/0106078

The final paper is better formatted (particularly concerning the figures):

https://doi.org/10.1103/PhysRevA.65.033818

It's discussed there on page 2+3 (Eq. (7)). That's, of course, for the setup without the QWPs in the slits.

It's also physically plausible: Concerning its momentum state the signal photon is pretty well coherent, i.e., has a pretty small width in momentum and thus can interfer. It's of course completely unpolarized, but this doesn't affect the diffraction interference pattern in the double-slit experiment.

For a didactical presentation (slides of my habilitation colloquium), see

https://itp.uni-frankfurt.de/~hees/publ/habil-coll-talk-en.pdf