Can the Quantization Axis of an Atom Affect its Spectral Emission?

[Niles]

Hi

Please see the attached picture. It shows an atom, the filled black circle, which consists of a J=0 level (with m=0 sublevel) and J'=1 (with m' = +/- 1 sublevels). From the left is a nearly monochromatic laser impinging on the atom, which is linearly polarized along the same direction of the applied B-field. This situation will drive the Δm=0 transition, thus displaying a Lorentzian spectrum with FWHM given by the lifetime of the excited state (as a function of frequency).

My question is, what will happen if the direction of the B-field is changed with 90 degrees, i.e. it is now parallel with k? This of course changes the quantization axis.

My own suggestion is that I can always decompose the incoming linearly polarized light into two circularly polarized components of opposite helicity that drive the Δm = +/-1 transitions. But they will - contrary to the first situation - be Zeeman broadened.

1) Is my reasoning correct?
2) Say I want to model the spectrum numerically using a collection of atoms. Would it simply just be to take the spectrum for the Δm=-1 transition and add it to the spectrum for the Δm=+1 transition?

Thanks for the help in advance.


Niles.

 

[Niles]

Do I have to use the density matrix to find the emission spectrum for each transition?

 

[Niles]

OK, I have thought this over. First of all, I know my suggestion in the first post is correct. So the answer to question 1 is "yes".

Now comes the task of question 2, namely to find the Zeeman-splitted spectrums for the different transitions (p- and s-polarized light). I am thinking about using the optical Bloch equations, but I am not quite sure how to get the spectrum from these.

Have anybody done something similar before?

 

[M Quack]

1) yes, you are correct. Actually, if the magnetic field is strong enough you should see 2 lines corresponding to m'=-1,1. To the best of my knowledge the m'=0 transition is forbidden in this case.

2) The absorption of different atoms should be incoherent, i.e. you just sum over the spectra of the different atoms.

One way of looking at the Maxwell-Bloch equations is to find the equilibrium densities as function of detuning.

You should be able to work out the emitted intensity as function of detuning from the population of the excited state and the time constant of the exponential decay. I would just calculate the spectra for m'=+ and -, and then sum them.