# How should two-photon transitions be modelled? Is second-order perturbation theory required? Or are sequential first-order processes sufficient?

For example, I want to consider the following situation: photon transit from $$m$$ energy level to $$m+2$$ after absorption of two phonons with frequency $$\Omega$$. I want to calculate a transition rate for this process and now I'm little stuck in the choosing the way to do it. Should I use a second-order perturbation theory to find this rate, or can I just multiply the probabilities as a sequential processes ($$m \to m+1 \to m+2$$ states) to find total probability? Which of these options is more correct?

• A sequential process would emit photons with very sharply defined energies, whereas in the 2nd order process, the photons' energies could divide up more flexibly. – Bert Barrois Jun 15 at 11:22

• To be more specific, photon initially have frequency $\omega$, my beam passing through the crystal, so the time of perturbation is, for example, $\tau = \frac{Ln}{c}$, where $L$ - length of the crystall in the direction of laser propagation. If we consider two phonon process, then photon can transit on levels $m \pm 2$ (besides other levels) with defined energy through $m\pm1$ level. So what are the difference in using SOPT and sequential processes in this case? – Kirill Jun 15 at 11:28