Exploring the Impact of Photon Polarization on Electron State Changes

[msumm21]

TL;DR Summary

How does the polarization of a photon impact the state change of an electron that absorbs it

How does the polarization of a photon impact the state change of an electron that absorbs it? Presumably the change of an electrons state (including spin) differs based on the polarization of the photon it absorbs.

 

[Vanadium 50]

Polarization is the direction of the electric field. It's the direction the electron moves if the photon isn't absorbed. Absorbtion just complicates matters.

 

[PeterDonis]

Polarization is the direction of the electric field.

Not in QM. In QM polarization is the spin of the photon. Which will in turn change the spin of the electron if the electron absorbs it. (Restrictions on what spin the electron can have also restrict what photons a particular electron can absorb.)

 

[PeterDonis]

Presumably the change of an electrons state (including spin) differs based on the polarization of the photon it absorbs.

Your presumption is correct.

 

[msumm21]

Thanks. Are there some simple examples available like
1. if a photon has polarization state X it can't be absorbed by an electron with spin Y
2. if a photon with polarization X is absorbed by an electron with spin Z it will change the electron's spin to U

 

[PeterDonis]

Are there some simple examples available

For free electrons, not really, because it's not really possible (at least not with our current technology) to observe a single free electron absorbing a single photon.

For electrons in atoms, we can at least observe transitions as spectral lines (although even then we're observing transitions in many atoms in, say, a gas, not just one atom), but I don't know how much experimental work has been done on this with light that has particular polarizations.

I believe many QM textbooks discuss the basic theoretical framework involved for electrons in atoms emitting and absorbing photons and the spin selection rules involved.

 

[vanhees71]

A single free electron can never absorb a single photon. It's kinematically impossible, i.e., you can't fulfill energy-momentum conservation and the on-shell conditions for electron and photon. Indeed in almost all textbooks on quantum mechanics you find at least the dipole selection rules derived.

 

[WernerQH]

Thanks. Are there some simple examples available like
1. if a photon has polarization state X it can't be absorbed by an electron with spin Y
2. if a photon with polarization X is absorbed by an electron with spin Z it will change the electron's spin to U

Feynman's Lectures on Physics, vol. 3, ch. 18-1 on electric dipole radiation.
Or (more fleshed out): Gordon Baym, Lectures on Quantum Mechanics, pp. 281ff.

 

[Cthugha]

For electrons in atoms, we can at least observe transitions as spectral lines (although even then we're observing transitions in many atoms in, say, a gas, not just one atom), but I don't know how much experimental work has been done on this with light that has particular polarizations.

I believe many QM textbooks discuss the basic theoretical framework involved for electrons in atoms emitting and absorbing photons and the spin selection rules involved.

Bransden and Joachain discuss this in quite some detail in their book on the physics of atoms and molecules.

However, I would like to point out one thing that people often are not aware of: You cannot simply flip a spin using photon absorption. In dipole approximation (and also beyond) the interaction matrix element is proportional to r and acts only on position space, not on spin space, so there is no direct interaction. The magnetic part of the light field would of course work in principle, but is far too weak in any realistic scenario.
If spins are indeed flipped by optical means, in most cases the process involves spin-orbit coupling which provides some kind of link between position space and spin space.

 

[WernerQH]

You cannot simply flip a spin using photon absorption.

What about NMR? Or are you reluctant to talk of photons at radio frequencies?

 

[Vanadium 50]

Not in QM. In QM polarization is the spin of the photon.

A. The correspondaance theorem says these are (statistically) the same thing.
B. In QM you can have polarization states that are admixtures of spin states,

 

[Cthugha]

What about NMR? Or are you reluctant to talk of photons at radio frequencies?

Sorry, for being unclear. I was interpreting the initial remark about spectral lines to imply atomic transitions that change the principal quantum number. For magnetic dipole transitions, these are forbidden in the non-relativistic case, but become weakly allowed due to relativistic effects (spin orbit coupling). Magnetic dipole transitions such as hyperfine transitions or Zeeman transitions that do not change the principal quantum number are not subject to this limitation.