Can the wavefunction of a photon be spread out to enhance the probability of 2-photon absorption?

Question

Assuming a beam of light as a collection of photons moving in some sort of "grid" with an average length between them, I can understand why increasing the light intensity is so critical to 2-photon absorption. We need the photons to be close enough together that their probabilistic absorption in space and time is close enough together that a molecule can absorb 2 at once.

My question is: Rather than needing to bring all the photons very close together (i.e., high intensity), would it be possible to instead pass all the photons through some sort of "scrambler" (some kind of scattering?) where their wavefunctions become spread out enough in space (or time) to increase the likelihood that 2 photons can be simultaneously absorbed?

Answer 1

Unfortunately, the picture with photons traveling in a grid is completely wrong in this case. The high intensity is crucial for the 2-photon process because the probability of the interaction is $\propto I^2$. For that reason for low intensities, the chances are also low, lower than for single photon process ($\propto I$).

That relation is derived from the principles of how your system is interacting with light, without considering photons as individual "balls". What is rather used are amplitudes of your fields that in the process of absorption are coupling two levels.