Originally Posted by

**KJW**
If the emission has a Lorentzian distribution of a given width, would the corresponding absorption also be a Lorentzian distribution of the same width? Microscopic reversibility suggests that it would.

Yes you are of course right. I was just trying to make a point that putting second atom in the way is basically momentum measurement which does projection onto eigenstates. In real case the absorption line would serve as "characteristic function of detector" or whatever is correct english expression. The result of experiment would be given by convolution of characteristic function of detector with signal if that makes sense. (In simplified case characteristic function is just delta function.) Sorry for my sloppiness.

Originally Posted by

**exchemist**
Might this not depend on the radiation environment of the emitting and receiving atoms? I seem to recall the uncertainty in the energy gap is related to the lifetime of the excited state - which I would have thought would be influenced by both the spontaneous and the stimulated emission rates, with the latter being influenced by the radiation flux to which the atom is exposed. But it was a long time ago and my memory may be faulty.

Yes you are exactly right. Quanitative description would be like this. Let

be coherent Hamltonian and

- imaginary part of selfenergy. Full Hamiltonian is then

. Let

be wavefunction of excited state (I will omit increase in population of ground state). Then time evolution in Schrodinger picture is like this.

therefore

.

Fourier transform of this gives Lorentzian.

From population of exited state one can say that time of life of excited state is

.

Originally Posted by

**exchemist**
This is an interesting thought experiment. Would what you are saying mean that the dispersion caused by a prism would have the effect of making the **probability** of absorption by the second atom** lower** than it would have been for a photon travelling directly, with no prism in between?

Yes of course because you are basicaly saying that you will change direction of every photon (here meant planewave) with wrong frequency. While atom would in principle be able to absorb it thanks to width of absorption line the photon simply won`t be there. Since real state of light is superposition of planewave photons you are sending probabilistic wave components in wrong direction.

There is one more freakish aspect though. If you will spread the wave packet by prism you can then rejoin different components of that wavepacket with some mirrors. What is freakish is that these probabilistic waves will interfere even if you send one photon (here meant real state of light) at a time.