# Linear Polarization of Single Photon?

I've heard it said (a while ago) that we don't usually speak of a single photon being linearly polarized or unpolarized, but rather we can speak of an ensemble of photons that are linearly polarized or unpolarized.

Is this still the current thinking in Quantum Optics?

If a Mach-Zehnder interferometer had one path that included an optical element that rotated the polarization by 90 degrees, then I think polarized light going through this filter wouldn't interfere, but unpolarized light would. Is this the case?

When the light intensity was high, the classical explanation would be that light from one polarization was interfering with light from another polarization.

But when the intensity is low enough that there are single photons passing through this interferometer, I suspect there would still be interference effects.

If so, would this mean that would could then talk about individual unpolarized photons?

I've heard it said (a while ago) that we don't usually speak of a single photon being linearly polarized or unpolarized, but rather we can speak of an ensemble of photons that are linearly polarized or unpolarized.

Is this still the current thinking in Quantum Optics?

No. It is perfectly possible to assign polarization states to single photons. There is no need for ensembles in order to talk about polarization.

If so, would this mean that would could then talk about individual unpolarized photons?

Yes, you can indeed talk about individual unpolarized photons, i.e. single-photon states of the electromagnetic field which do not have a well-defined polarization. This is not a pure state, though: it is a maximally mixed state, within the span of two different modes that are identical except for having orthogonal polarizations.

If a Mach-Zehnder interferometer had one path that included an optical element that rotated the polarization by 90 degrees, then I think polarized light going through this filter wouldn't interfere, but unpolarized light would. Is this the case?

No, this is not the case. Polarized light won't interfere, and neither will unpolarized light. This holds for both classical light and single-photon sources.

When the light intensity was high, the classical explanation would be that light from one polarization was interfering with light from another polarization.

No, that's incorrect. In unpolarized light there is no coherence between the two orthogonal polarization components. The polarization-rotation element does take the light polarized along $$x$$ and puts it in yuxtaposition with the original $$y$$-polarized light from the other arm, but since there is no coherence between the two, they won't interfere.

• Thank you for clarifying. Follow up question, is there an experiment that has the idea I was going for, something that will produce one result with single unpolarized photons and a different result for polarized ones? – David Elm Oct 22 '19 at 16:03
• That's basically too broad to say anything useful other than trivial proposals. What's wrong with passing the photon through a polarizing beam splitter? (i.e. if you want to distinguish between H-polarized and unpolarized photons, pass it through a H-vs-V PBS and look for hits on the V port.) – Emilio Pisanty Oct 22 '19 at 16:06
• I'm generally fascinated by the quantum optics experiments that can be done with various set-ups. Paul Kwiat has some very cool work with interaction-free measurements. physics.illinois.edu/people/kwiat/… So I was trying to think through if there was a nice experiment that could distinguish between a photon that was polarized, but whose polarization was (classically) unknown, and a photon from an unpolarized source. – David Elm Oct 22 '19 at 16:29
• @DavidElm If you have specific questions I can try to address them. If you are just interested in general discussion, take it to Physics Chat. – Emilio Pisanty Oct 22 '19 at 16:32