Will an atom emit a polarized photon the same as the polarization of the incident photon?

Question

So say you have a vertically polarized single photon impinging on an atom. The atom absorbs the photon and re-emits it. Does the re-emitted photon have the same polarization (vertical) as the incident photon? My gut tells me it does not, but I do not know.

I remember reading in a QFT book that the free photon has an inherent circular polarization to it, so does that mean the emitted photon will be circularly polarized? (Is this even correct?) (I am not super knowledgeable in QFT, but I have had a good amount of QM courses)

Answer 1

This is not a full answer, as I only know about hydrogen, but here the answer is "Not necessarily".

When photons close to the resonance of the 1→2 transition, i.e. the so-called Ly$\alpha$ photons, scatter on neutral hydrogen, they may become polarized. The amount of polarization depends on whether the energy of the photon is very close to the line center ("core scattering"), or farther away ("wing scattering"), as well as on the angle $\theta$ between the incident and outgoing photon.

The phase function — i.e. the probability distribution that determines the angle of scattering — also determines the degree of polarization. For instance, for core scattering this is $$ W(\theta) \propto 1 + \frac{R}{Q} \,\cos^2\!\theta, $$ where $R/Q$ is the degree of polarization for 90º scattering.

I won't go into too much detail if this is not what you had in mind, but it turns out that this can result in either unpolarized or partially polarized photons, which in general is different from the polarization before the scattering event.

If this is of interest to you problem, I can elaborate a bit on this.

Answer 2

So say you have a vertically polarized single photon impinging on an atom.

You cannot vertically polarize a photon. The photon has spin 1 which, because the mass of the photon is zero, will be either +1, i.e. in its direction of motion, or -1, against its direction of motion. The photon does not have an electric and magnetic field defining it so as to talk of classical polarization. Only momentum and $E=hν$

This can be seen pictorially in how photons build a polarized beam :

Note how the photon spin is + or - to its direction of motion, while the light has circular polarization.

The atom absorbs the photon and re-emits it. Does the re-emitted photon have the same polarization (vertical) as the incident photon? My gut tells me it does not, but I do not know.

Cannot be vertical for the individual photon, so the answer is no. If a photon with spin +1 is absorbed by an atom can give a photon of spin +1 to its direction of motion when it deexcites, will depend on the energy levels involved, i.e. the angular momenta for the individual energy levels and atoms.

Light, the quantum mechanical superposition of zillions of photons can have vertical (to its direction of motion) and circular polarization, depending how the individual wavefunctions of the photons $Ψ$ are added into one wavefunction for the ensemble. This link shows how the classical field is built up from the quantum mechanical fields.