Phenomenology of photon pair production in non linear crystals Could anyone describe the mechanism that produces photon pairs when a beam of light incides on a non linear crystal? 
I'm aware of the conservation arguments than can be made with the two produced beams in relation to the original beam, but the actual mechanism by which a photon "turns" into a pair of photons eludes me.
 A: You can read a lot of questions about splitting photons, but contrary to popular belief you cannot split a photon into two photons.
What really happens inside the crystal is that the original incident photon gets absorbed:


*

*either by a single atom/electron system inside the crystal

*or by the molecules/the crystal lattice
Thus, the incident photons ceases to exist as a photon and gets converted into the energy of the atom/electron system or molecules of the crystal lattice.
Consequently, something called (cascade) two photon emission happens. These photons' emission can happen from:


*

*either a single atom/electron system


in this case the single atom/electron system emits the originally absorbed total energy in two steps, cascades.
https://arxiv.org/pdf/1502.04349.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0022231310003017


*from different locations inside the crystal lattice



However, a new nonlocalized mechanism for the production of correlated photon pairs in SPDC has highlighted that occasionally the individual photons that constitute the pair can be emitted from spatially separated points.[17][18]

https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

In principle,
  this effect enables a pair of correlated photons to emerge
  from two spatially separated origin points, and this introduces new positional uncertainty of a fundamental quantum
  origin. In the following analysis, using a quantum electrodynamical (QED) formalism, we fully account for both
  localized and nonlocalized emission.

https://ueaeprints.uea.ac.uk/id/eprint/63173/1/PhysRevLett.118.133602.pdf
