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While trying to understand polarization in quantum field theory, I wondered how a single photon could go through a linear polarizer. I found a paper which asked "Is a single photon always circularly polarized?"

This paper proposes an experiment to determine if a single photon can be linearly polarized, or if only pairs of photons can be linearly polarized. It suggests that there may be non-trivial consequences regarding all Bell experiments with a "linearly polarized single photon" (because such thing may not exist).

The paper is from 2014 and the experiment seems simple if you have the right equipment, so do we have the result of the experiment yet?

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    $\begingroup$ For what it's worth, that preprint is unpublished, and didn't make it into the special issue it was submitted to. That doesn't invalidate the science but it's a warning flag to be aware of. $\endgroup$
    – Emilio Pisanty
    Commented Oct 18, 2015 at 11:43
  • $\begingroup$ @darkblue if $c_{\vec{k}}^{R/L}$ is the creation operator of a photon with momentum $\vec{k}$ and helicity $R/L$, try this creation operator now (and prove that this is a creation operator): $(c_{\vec{k}}^{L}-c_{\vec{k}}^{R})/\sqrt{2}$. I recommend you to study second quantization grounded on quantum mechanics. Second quantization is only a better way to deal with quantum systems, and some cases the only way (when the number of particles do not commute with some observables) $\endgroup$
    – Nogueira
    Commented Oct 20, 2015 at 16:28
  • $\begingroup$ @darkblue In special relativity, the number of particles of mass $m$ does not commutes with observables distributed in small boxes ($~\frac{\hbar}{mc}$). So second quantization is needed. $\endgroup$
    – Nogueira
    Commented Oct 20, 2015 at 16:34
  • $\begingroup$ @Nogueira About your small boxes : I would argue this is a first quantization issue. By speaking about "particles with masses in SR" you are gauge fixing yourself in momentum space. Then you talk about position space by saying space boxes. Obviously it won't commute but not because of the number of particles. Your bad choice of basis is not a reason good enough to justify needing second quantization (a conceptual jump in a higher function space). I think the experiment proposed in the paper is the analog of bell's experiments but for second quantization, a way to know if the jump is needed $\endgroup$
    – darkblue
    Commented Oct 20, 2015 at 22:13
  • $\begingroup$ @Nogueira I think I can conceptualize quantizations correctly. Suppose we have a set S , f : S -> S , g : L2(S) -> L2(S) ,h : L2( L2 (S) ) -> L2( L2( S ) ) , then There are several interesting ways we could sample from S We start by picking a s0 in S, then f^n (s0 ) . Or we could start by picking ls0 in L2(S) then g^n(ls0) from which we sample an element which is in S : analog to first quantization Or we could start by picking lls0 in L2(L2(S)) then h^n(lls0) from which we sample an element which is in L2(S) from which we sample an element which is in S : analog to second quantization $\endgroup$
    – darkblue
    Commented Oct 20, 2015 at 22:27

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For a single photon, the only similar physically meaningful question is whether the circular polarization is left-handed or right-handed. Quantum mechanics may predict the probabilities of these two answers. An experiment, a measurement of L/R, produces one of these answers, too. After the measurement, the photon is either left-handed or right-handed circularly polarized.

If a photon is prepared in a general state, it has nonzero probabilities both for L and R. In such a "superposition", we may perhaps say that the single photon has no circular polarization. This statement means that we are uncertain which of the polarizations will be measured if it is measured. But when the circular polarization is measured, one always gets an answer, according to the result of the measurement.

Linear polarizations are the simplest nontrivial superpositions of L and R. The absolute value of both coefficients, $c_L$ and $c_R$, is the same while the relative phase encodes the axis on which the photon is polarized.

The paper quoted in the question is completely wrong. An example of a very wrong statement is that the linearly polarized photon moving in the $z^+$ direction carries $J_z=0\cdot\hbar$. In reality, a linearly polarized photon or any photon is certain not to have $J_z=0\cdot\hbar$. A linearly polarized photon has the 50% probability to be $J_z=+1\cdot\hbar$ and 50% to have $J_z=-1\cdot\hbar$. The expectation value $\langle J_z\rangle = 0$ but it's still true that the value $J_z=0\cdot\hbar$ is forbidden.

A different question is the polarization of an electromagnetic wave. For a wave, e.g. light, one may distinguish left-right and right-handed and $x$-linearly and $y$-linearly and elliptic polarizations of all kinds one may think of. In terms of photons, a macroscopic electromagnetic wave is the tensor product of many photons. If all these tensor factors are linearly (or circularly) polarized, then the wave may be said to be linearly (or circularly) polarized. Because the polarization of the whole wave requires some correlation in the state of individual photons, a wave may be measured not to be circularly polarized in either direction. But an individual photon is always circularly polarized in one of the directions when the answer to this question is measured.

The paper may present a proposed experiments which may be done but what is completely invalid is the author's interpretation of this experiment – even "possible interpretations" before the experiment is actually performed. The correct description by quantum mechanics isn't included among their candidate theories with which they want to describe the experiment.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – David Z
    Commented Oct 21, 2015 at 6:55
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Answering my own question to close a far too long debate that heated far too much in my opinion.

To sum up :

According to mainstream physics, quantum mechanics : No, a single photon isn't always circularly polarized. See Lubos's good answer if you want more details.

The paper is unorthodox science, as it proposes a test to falsify in quantum mechanics.

A little advice to any beginners to the field like me, be aware that because there has been many unsuccessful attempts to falsify QM in the past, any talking about any new experiment to falsify and you will be looked upon as crackpot.

A little QM self fulfilling prophecy joke to end on a more light tone : "Obviously because we live in a QM world, any experiment that would falsify QM can not happen" :)

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    $\begingroup$ Proposing experiments to falsify QM does not automatically mean that you're a crackpot. In fact, pretty much everyone in quantum foundations is to at least some extent unhappy with the situation, and if we found an experiment that actually broke QM then most people would be ecstatic - it would give us an upper hand on the beast. Indeed, there have been many serious attempts to falsify QM (does Bell ring a bell? when Aspect set out to do the measurements, he set out to show that common sense would hopefully triumph over QM) but what this means is that (cont.) $\endgroup$
    – Emilio Pisanty
    Commented Oct 24, 2015 at 9:38
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    $\begingroup$ all the easy approaches have already been used, and if you want to propose a new one you had better bring something nontrivial to the table. Papers that say "I don't like QM, this other theory is better" will generally be met with "well, how does your theory deal with $X$"?, and there is a large set $\{X\}$ of situations that QM explains perfectly and your new theory needs to satisfy. $\endgroup$
    – Emilio Pisanty
    Commented Oct 24, 2015 at 9:44
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    $\begingroup$ This particular paper makes some pretty crude mistakes (e.g. it ignores that number-resolving detectors are easy to implement now) which means that its alternate theory isn't really a workable explanation for the current experimental state of the art. That makes it hard to take seriously as an experimental proposal. $\endgroup$
    – Emilio Pisanty
    Commented Oct 24, 2015 at 9:46
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At the quantum-mechanical level this article supports Luboš Motl‘s answer above that a single photon—regardless of wavelength and energy—is always circularly polarized either right-handed or left-handed when measured.

The question, which hinges on phase, was marked as answered many years ago, however the debate rages on about what a single photon actually looks like “in flight”, ie. before it’s measured. The paradox is that measurement collapses the wave function. Trying to work around this paradox, Radosław Chrapkiewicz and others published “Hologram of a single photon” in Nature July 2016, pre-publish (free) version here.

The authors begin their paper by acknowledging how challenging it is to retrieve information that characterizes a photon due to the “entirely indeterminate global phase following from the perfect rotational symmetry of their Wigner functions in the phase space.”

They designed an experiment to measure information from 2000+ single photons arriving over time, where each detected photon was one of a two-photon polarization-entangled pair. The accumulated results built a hologram they feel more closely represents that of a single photon:

Encoding the local phase of quantum wavefunction in the hologram of a single photon

At the very least, the holographic depiction of a single photon adds to the commonly-seen illustrations of light-also used sometimes to depict a single photon- dating from James Clerk Maxwell’s era and still widely used today, and which some find confusing and counterintuitive:

Maxwell-era cartoon of light wave, including for single photon

Even if it works for a superposition of at least two photons, it’s much less clear how it could represent a single photon as it looks more like a standing wave than a traveling wave. To readers wondering how both the electric and magnetic fields of a traveling wave can simultaneously be zero for multiple photons see this question and its responses.

As readers of this question are most interested in single-photon representation, the following helical illustration (or its mirror) is, according to the first-referenced article, a more helpful representation of an individual photon:

Individual photons are always left or right circular

Representations of a single photon, if the “always circularly polarized” view is the correct one, reveal that projections on each plane would be more accurately drawn 1/4 wavelength translated from each other:

looking at one helix from aside and above

However, if applied to single photons, all the cartoons imply an infinite length to single photons which is not supported by experiment, reminding us that all illustrations have limitations.

This article claims the debate is over the other way, that experiments prove single photons can absolutely be linearly polarized.

@darkblue accepted a “no” answer nearly 7 years ago, yet it seems more likely that the debate will continue, and hopefully adding new experimental results will help provide balanced context to future-askers of the same question.

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There is a big misunderstanding about what is the spin of a photon. The orthogonal standing B- and E-field could have a left hand orientation or a right hand orientation (see last page in this elaboration).

For polarizers it is important only, how the photons E-field is orientated to the slits, in the case of 0° and 180° photons of both spin orientations are going through. (And artfully designed polarizers rotate photons with +/- 45° to the above mentioned orientations, so one get 50% transmittivity.)

For photons, going through birefringent calcite, the spin orientation play a great role. The calcite separates the two spin orientations. This is clear because even polarized light will be divided into two beams.

Circular orientated light has got a rotational momentum from the source emits it. The E- and B-field rotating together. Of course one could feel free to represent linear polarized light as a superposition of a clockwise and an anticlockwise rotating state. But this mathematics one is able to do with the state of a football too.

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    $\begingroup$ This is a classical picture. I was looking for a quantum field picture. The question I was asking is : can a quantum field with a single quanta of energy make its Left Handedness, and Right Handedness interfere to behave as a linearly polarized quanta of energy. I was looking for the physical result (real data) of the experiment proposed in the paper. $\endgroup$
    – darkblue
    Commented Oct 18, 2015 at 20:53

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