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Reading from Introduction to Nonlinear Laser Spectroscopy - Revised Edition (1988) by Marc D. Levenson and Satoru S. Kano (p13-14, bold emphasis mine):

Consider a medium in which each atom can absorb only one definite frequency, but in which different atoms can absorb different frequencies. Such a situation can result, for example, from the Doppler effect which allows atoms moving away from a light source to absorb a frequency below that absorbed by atoms moving toward the source. The absorbed frequencies, however, are the same in the rest frame of each atom. The absorption lines of such a medium are termed inhomogeneously broadened, because different atoms are responsible for different portions of the absorption line. If any frequency within the absorption band could excite every atom with the same probability, the line would be homogeneously broadened. Such a situation can occur in an atomic beam where the atomic velocities are perpendicular to the direction of propagation of the light [22].

I don't understand what the bold text is referring to. It seems there must be a rest frame in which the absorbed frequencies are different, or there would not be inhomogeneous broadening (from the perspective of the instrument). In what sense are the absorbed frequencies the same?

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  • $\begingroup$ I think you are just misunderstanding the grammar. The author refers to the rest frame of each individual atom, i.e. suppose you have 10 atoms, then in these 10 individual rest frames, the resonance frequency will have the same value. The author does not talk about an observing reference frame where all atoms have the same resonance frequency at a given time. $\endgroup$ Jan 14 '20 at 21:19
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It means that each atom sees the incident radiation in its own frame. So suppose the atom has an absorption line at 500 THz. And you shine a laser at it at 500.1 THz (as measured in your frame).

Then the atoms that are moving toward you are going to see a slightly higher frequency than you measured (say 500.2 THz). So they won't absorb this light.

But the atoms that are moving away from you are going to see a slightly lower frequency than you measured. For the ones that are moving away at just the right velocity, it will be 500.0 THz, and they will absorb the light.

Since we can distinguish atoms that are moving in one direction from atoms that are moving in another direction, the atoms that can absorb your light are a distinct population from the ones that can't absorb your light, and so we call this an inhomogeneous broadening effect.

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