I 3 photon transfer probability

Malamala
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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?
 
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Two photon microscope has been a familiar apparatus. I suppose you can get some insight from it.
 
Similarly, third-harmonic generation is a well-studied phenomenon with lots of references available.
 

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