Optical density of man atomic ensemble and linewidth

Niles

Hi

I've been thinking about something for a while now. If I take a two-level atom, completely at rest, then I can probe it with a quasi-resonant laser. The absorption of the atom is a nice Lorentzian, nothing fancy here.

However, now say I take 10¹¹-10¹² atoms. The specific number doesn't matter, all I am trying to do is to probe the system in a regime where the optical density has increased very much. For the sake of clarity I assume the atoms to be completely independent and at rest. No collisions/dephasing/... occur between them.

If I now probe this system, will I still see an absorption Lorentzian with the same FWHM as in the single-atom case? Or will the transition be broadened somehow?

The reason why I believe it should be broadening is because I keep thinking about, e.g., my table (or any other macroscopic object, a pencil, calculator, ...). It has an optical depth that is very large, so the absorption profile is also extremely broad. I was wondering if the same holds for an independent atomic ensemble.

I've been trying to look at the Optical Bloch Equations to see if such a behavior could occur, but it is not immediately clear that it is so. Is my analogy wrong?

Best,
Niles.