I Why can’t photons “pile up” to eject an electron?

[Kostik]

TL;DR Summary

Why doesn’t the bosonic character of photons prevent the photoelectric effect?

The photoelectric effect is essentially the observation that light below a certain frequency cannot ionize an atom, no matter how large its intensity. Einstein explained this in 1905 by postulating that light consists of particles (photons) with energy proportional to their frequency.

However, photons are bosons (spin-1) and therefore any number of photons can occupy the same quantum state. Therefore, in very high intensity light, it seems plausible that two or more photons in the same state can combine their energies to ionize an atom.

Apparently, this is not the case, as the photoelectric effect makes clear. Why?

 

[willyengland]

A multi-photon absorption might happen I think under extreme conditions like a strong laser.

 

[Demystifier]

If you draw the Feynman diagrams for absorption of one and two photons, you see that they have one and two vertices, respectively, so the latter is suppressed because it is a higher order in the perturbative expansion in $\alpha$.

 

[DaveE]

Multiphoton imaging is a well established tool. Here's a review for GI docs, for example.
https://pmc.ncbi.nlm.nih.gov/articles/PMC3218135/

If you can use this to reach higher excited states I'm sure you could ionize an atom too. But I don't see why you would want to. Just use a shorter wavelength laser, they're cheaper, easier.