Why is it called "rotating wave approximation"? I am just wondering why it is called rotating wave approximation? Where does the rotating come from? According to wikipedia, it says

"Since in some sense the interaction picture can be thought of as rotating with the system ket only that part of the electromagnetic wave that approximately co-rotates is kept; the counter-rotating component is discarded."

Unfortunately I couldn't get it. Can anyone expain it more clearly?
 A: The point is that the terms "rotating" or "counter-rotating" do not refer to any physical rotation at all, they refer to rotation in the complex plane. That is because if you take a look at the complex exponential $e^{i \omega t} = \cos(\omega t) + i \sin(\omega t)$, and draw the shape it makes in the complex plane, you see that it traces a circle with a frequency $\omega$.
The starting point of the "rotating wave" approximation is then to take a look at the quantum state of the unperturbed system (e.g. the atom) and identify with which frequency does it rotate in the complex plane. A perturbing photon will have a particularly strong effect if its state is rotating in the complex plane with a frequency that is close to this frequency. However, a real photon beam (such as from a laser) will have a 50/50 superposition of photons that rotate with a frequency $\omega_L$ and minus $\omega_L$ in the complex plane. The basic idea of the "rotating wave" approximation is to assume one of the two frequencies is close to that of the frequency of the state of the system and discard the second half.
So one could perhaps call the approximation as "co-oscillating wave approximation", with the discarded part of the impinging state to be called "counter-oscillating". Either way, I think it should be clear what the point is.
A: The wording is bad. As far as I can find in the literature, it was introduced by Rabi in '38, who simply observed it experimentally. Since he replaced a linear field with a rotating one, it should be called "rotating field approximation". The first paper I can find calling it a "rotating wave approximation" is by Lamb in '58. I think this term comes from the "rotating wave function" which is used when going into a rotating frame, but the approximation is actually independent of the frame, so it is not a good name.
