Some Non-Perturbative and Non-Linear Effects in Laser-Atom Interaction
  We show that if the laser is intense enough, it may always ionize an atom or induce transitions between discrete energy levels of the atom, no matter what is its frequency. It means in the quantum transition of an atom interacting with an intense laser of circular frequency $\omega$, the energy difference between the initial and the final states of the atom is not necessarily being an integer multiple of the quantum energy $\hbar\omega$. The absorption spectra become continuous. The Bohr condition is violated. The energy of photoelectrons becomes light intensity dependent in the intense laser photoelectric effect. The transition probabilities and cross sections of photo-excitations and photo-ionizations are laser intensity dependent, showing that these processes cannot be reduced to the results of interactions between the atom and separate individual photons, they are rather the processes of the atom interacting with the laser as a whole. The interaction of photons on atoms are not simply additive. The effects are non-perturbative and non-linear. Some numerical results for processes between hydrogen atom and intense circularly polarized laser, illustrating the non-perturbative and non-linear character of the atom-laser interaction, are given. 
Qi-Ren Zhang