Two conditions are necessary. If Ei is the ionization energy, to have the absorption of N photons to obtain ionization it should be Nhv > Ei. The problem is that the probability of the absorption is proportional to the I^N. where I is the laser intensity, or any quantity related to it (only changes the constant coefficient), therefore, you need enough photon flux to initiate the process.

Gianpiero, thanks. should be proportional to I^(-N), right?

sorry. ~I^N.

Yes this last one

An example of detailed evaluation of two-photon ionization is described in the paper "Two-photon ionization of an atom by photons from different beams" by L. F. Vitushkin, A. I. Mikhailov in "Optics and spectroscopy", 1981, v.50, No. 1, pp 4-8.