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Quantization axis

  1. Jul 14, 2012 #1
    Hi

    I am looking at a bunch of atoms in a homogeneous magnetic field, irridiated by a monochromatic EM wave. I am trying to figure out how to intensity pattern of the emitted light by the atoms looks.

    Case 1) I have attached a picture of the situation called "case_1.jpg". It is very clear that only π-transitions are being driven, i.e. Δm=0 transitions.

    Case 2) I have attached a picture of the situation again. The quantization axis points along the magnetic field, but the polarization is orthogonal to it. So somehow I need to decompose the polarization into something in the same plane as the B-field. How can I do that?

    I would be very happy to recieve some feedback.

    Best,
    Niles.
     

    Attached Files:

  2. jcsd
  3. Jul 14, 2012 #2
    Ah, ok. I think I figured it out entirely by myself. I can of course always decompose it into circularly polarized light along k. So they will drive the Δm=+1 and Δm=-1 transition. But then what happens when B is perpendicular to both k and E? Then my "trick" doesn't work anymore.



    Best,
    Niles.
     
    Last edited: Jul 14, 2012
  4. Jul 14, 2012 #3
    Maybe that is a forbidden transition.
    Or maybe you better look at quadropole moments, or magnetic dipole moments.
    I thought that the m=0 transition is dipole forbidden, anyway.
     
  5. Jul 14, 2012 #4
    I'm pretty sure having E perp. to k perp. to B will still yield a signal. I just don't see how I can ever decompose E into something along B, but I know it is possible.
     
  6. Jul 17, 2012 #5
    You can still decompose the linear polarization into two circular ones. What changes wrt case_1 is the relative phase between the two circular waves.

    Therefore you should get the same spectrum as in case_1, i.e. delta-m=0.
     
  7. Jul 18, 2012 #6
    Hi

    Thanks for replying! However I have to disagree. So B is perp. to k, which is perp. to E: If the electron is oscillating circularly along B, then looking "edge on", it looks linear. And it is exactly this motion that the E-field excites. So the transitions being driven are delta-m = +/- 1.

    Does this sound reasonable to you?
     
  8. Jul 21, 2012 #7
    When I find a moment I will work this out in detail.

    You can write the dipole operator ε.r as Ʃ_m |r| ε_m Y_1,m
    where m=-1,0,1 and Y_1,m is a spherical harmonic.

    The matrix element then reduces to an amplitude prefactor and some
    Clebsch-Gordans. If you know the initial and final angular momenta
    this is easy to write down exactly.
     
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