(Potentially connected to this question, but could not find the answer to my particular question there.)
The frequency spread and time duration of a pulse are related by:
$$ \Delta \omega \Delta t \approx 2 \pi, $$
from which perfectly monochromatic radiation ($\Delta \omega$ = 0) would require an infinite "pulse", $\Delta t \rightarrow \infty$.
Now: let's think of a (locked) CW laser, emitting a stable frequency with a linewidth of ~10s of kHz. Actually let's even assume 0 linewidth, let's assume it's ideal.
I have a shutter (or some other sort of switch) in the beam path, that goes ON and then OFF in a very short amount of time (100s of µs). Because of the finite duration of the pulse, I now have a spread in frequencies, following the Fourier relations.
So there are photons with a little bit more and a little bit less energy than originally. How? What's the interaction that allowed the reshuffling in energy?