I'm currently looking at Rabi Oscillations, and not I have a look at the following equations:
$$W = \sqrt{\Omega^2+\delta^2}.$$
The amplitude:
$$\frac{|\Omega|^{2}}{\delta^{2}+|\Omega|^{2}}$$
Now, I see that if the detuning $\delta = (\omega – \omega_{0})$ is large, the two level approximation is bad, since the ratio between level 2 and 3 is getting closer to 1.
But why does the two level system not work for high $\Omega$?
Best Answer
In the classical Rabi oscillation, where you solve the Bloch equations to find the dynamics of your spin-1/2 moment, you ALWAYS use a two-level system. The system is best suited for that, independent of your detuning.
Why? Because the a spin 1/2 system, which has two levels, is representable in the Bloch-sphere, which shows up as the equivalence between the SU(2) group and the SO(3) groups.
The case, in which the classical Bloch equations won't be sufficient, is the case when you have spins more than 1/2 (so more than 2 levels), and your Hamiltonian would make higher levels interactions to each other (which is rare). So if you have spin-1 system, for example, then the Bloch sphere would not be enough to represent the dynamics of your system, because the Bloch-sphere looks only at the orientation of your system, which is a vector quantity that you classically represent by the Bloch vector. If you have a higher spin, then a contribution would show up from higher multipole moments, which is alignment rather than orientation, that are represented with higher order tensors $T^{(K)}$.
Luckily, even though higher multipole moments could exist in many atoms, their effect isn't really pronounced. The reason is that we usually use light to interact with atoms, and light as polarizations which could be either linear $(\pi)$ or circularly polarized $(\sigma^+,\sigma^-)$, or a superposition of those. Therefore the interaction of higher orders would only exist in a pronounced way if you push your system to have not only dipole transitions, but also quardrupole and octupole and higher order transitions.
The most complicated case with light is when you have linearly polarized light for pumping. In that case you'll induce alignment rather than orientation. A paper that discusses that is this:
http://arxiv.org/abs/physics/0605234
For more details, look at the irreducible representations of Multipole moments. It's a huge topic, into which I wouldn't recommend going, unless you have something to do with research. The article would give you an introduction into that.
Good luck, hope that helps.