3 photon transfer probability

[Malamala]

Hello! If I have a 2 level system with the energy difference between the levels $\omega$ and a photon source, producing $n$ photons per second, with a frequency $\omega/3$. What is the probability of having a 3 photon excitation and how can I derive it?

 

[anuttarasammyak]

Two photon microscope has been a familiar apparatus. I suppose you can get some insight from it.

 

[Andy Resnick]

Similarly, third-harmonic generation is a well-studied phenomenon with lots of references available.