Photon angular momentum and magnetic quantum number selection rules

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Discussion Overview

The discussion revolves around the selection rules for magnetic quantum numbers in the context of photon interactions with atoms, specifically focusing on the implications of polarization and the quantization axis. Participants explore the relationship between photon angular momentum, polarization states, and the resulting selection rules in both theoretical and experimental frameworks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that the electric dipole selection rules for magnetic quantum numbers require delta_m = -1, 0, or +1, and relate this to the conservation of angular momentum.
  • There is a discussion about the definition of the quantization axis, with some arguing it is arbitrary and set in the laboratory frame, while others suggest it should align with the direction of photon propagation.
  • One participant questions why delta_m = ±1 is not allowed for linearly polarized light, despite it being a superposition of circular polarizations.
  • Another participant clarifies that the polarization basis used for photons can affect the interpretation of selection rules, emphasizing the distinction between circularly polarized light in the lab frame and the atomic frame.
  • Concerns are raised regarding the projection of angular momentum for circularly polarized photons and its implications for selection rules.
  • There is an inquiry about the possibility of aligning the lab frame with that of the atom and the effects of using linearly polarized light in such a scenario.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the quantization axis and its relation to photon propagation. The discussion remains unresolved regarding the implications of aligning the lab frame with the atomic frame and the resulting selection rules for linearly polarized light.

Contextual Notes

Participants highlight the complexity of the relationship between the polarization of light, the quantization axis, and the resulting selection rules, indicating that assumptions about the frames of reference and polarization bases may lead to different interpretations.

  • #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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