Photon angular momentum and magnetic quantum number selection rules

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SUMMARY

The discussion centers on the electric dipole selection rules for magnetic quantum numbers in photon interactions, specifically that delta_m can only be -1, 0, or +1. The quantization axis is defined in the laboratory frame and is independent of the photon’s direction of propagation. Linearly polarized light does not allow transitions with delta_m = ±1 due to its representation in the polarization basis, where only the pi component induces delta_m = 0 transitions. This clarification resolves confusion regarding the relationship between photon polarization and angular momentum conservation.

PREREQUISITES
  • Understanding of electric dipole selection rules
  • Familiarity with quantum mechanics concepts, particularly angular momentum
  • Knowledge of photon polarization states (sigma and pi)
  • Basic principles of atomic transitions and quantization axes
NEXT STEPS
  • Study the implications of electric dipole selection rules in atomic physics
  • Learn about the role of quantization axes in quantum mechanics
  • Explore the differences between circular and linear polarization in photon interactions
  • Investigate the effects of optical pumping on atomic states and transitions
USEFUL FOR

Physicists, quantum mechanics students, and researchers in atomic and optical physics who are interested in photon interactions and selection rules.

  • #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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