What is Photon Phase? Explaining Confusions

[Talisman]

It occurs to me that I've probably been confusing "phase" in a number of contexts. In particular:

1) If we write a photon's polarization as $\psi = |x\rangle + e^{i\theta}|y\rangle$, then we can call $\theta$ a "phase."

2) When a photon bounces off a mirror, it picks up a relative phase of $i$. If I understand correctly, this is the same "phase" as above. It is also the "phase" referred to in the two-slit experiment.

3) Inside a Mach-Zehnder interferometer, after a beam splitter, we represent the state as something like $\psi = |0\rangle + i|1\rangle$. If I understand, the phase shift happens because of (2). But it's not clear to me in what sense "which-path" information has a phase.

And I should add:

4) We can perform the two-slit experiment with electrons and get a similar result. How can we explain it with "phase" (like we did in 2) if there's no polarization basis in which "phase" is meaningful?

Can anyone help me clarify?

 

[bhobba]

Unfortunately you are on the wrong track. I will let experts in quantum optics explain the detail of the interferometer etc, but exactly what a photon is is rather more complicated than can be described by the standard QM notation you are using.

See:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

If it even has a wavefunction is rather complicated, but with a surprising result:
https://arxiv.org/ftp/quant-ph/papers/0604/0604169.pdf

Thanks
Bill

 

[Talisman]

Thanks bhobba. I think most of that stuff is over my head though :(

From more reading, it seems that the photon version is a result of EM phase and the electron result is due to de Broglie wave interference.

Still hoping someone can enlighten me in very simple terms.