Photon angular momentum and magnetic quantum number selection rules

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The discussion centers on the selection rules for magnetic quantum numbers in photon interactions, specifically addressing why delta_m can only be -1, 0, or +1 for electric dipole transitions. The quantization axis, which is set in the laboratory frame, does not necessarily align with the direction of photon propagation, leading to confusion about the angular momentum projections of circularly and linearly polarized light. While linearly polarized light can be viewed as a combination of circular polarizations, it only allows for delta_m = 0 transitions due to its specific polarization basis in the lab frame. The conversation highlights the importance of understanding the polarization basis and how it affects the selection rules, emphasizing that the physical interpretation of these rules is tied to the chosen quantization axis. Ultimately, the nuances of photon polarization and angular momentum conservation are crucial for comprehending the selection rules in atomic transitions.
  • #31
I believe I have gained a much better understanding of the selection rules and how they are defined with and without an external field. I would like to thank all of you for your time in explaining these concepts.

I have a relevant question regarding optical pumping that perhaps you might be able to help me with (If it is deemed necessary, I can post this in a separate thread). Consider an atom with a simplified two-level system: ground state: J=½ (mJ =±½) and excited state J'=½ (mJ'=±½).

In an idealized situation with no external field (in other words, let us neglect the Earth's field), suppose I shine left circularly polarized (LCP) CW laser light at an ensemble of these atoms. (Here it is assumed that the wavelength of the light is resonant with the energy difference between the two levels.) Further suppose that I define my quantization axis as along (i.e. // to) the propagation axis of the light.

This light will induce Δm=+1 (i.e. σ+)transitions, and eventually drive all the atoms into the J=½, mJ=½ ground state after multiple absorption and relaxation cycles (i.e. optical pumping). This suggests that after pumping with this LCP laser light for some time, the atoms will become transparent to the light, since atoms in the J=½, mJ=½ ground state cannot absorb this light. This resulting change in opaqueness or transparency of the atoms over time can be easily monitored with a light-detection device like a photodiode or photomultiplier.

My question is: is there any fundamental reason against observing such an outcome in a physical experiment? Is there a requirement for an external field to be applied? I have come across a few threads online which suggest that a magnetic field is required.

Furthermore, in a real-life configuration, does the Earth's field affect these outcomes?
 

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