# How to measure the direction of circular polarization of single photons?

I just watched this video about the 2022 Nobel prize in physics which mentions the experiments that have been conducted to test Bell's inequality. In the video, they also described the experiment by John Clauser which used the following steps:

1. Calcium atoms are excited by intense light.
2. When transitioning back to the ground state, there is a transition that emits two photons and which leaves the atom's spin unchanged; thus, the photons must have opposite circular polarization (by the way, why can't the photons simply be linearly polarized?).
3. The two photons' polarization directions get measured independently.

I'm interested in the third point from above. How does one actually measure the direction of polarization for a single circularly polarized photon? In the video, they just say "passing photons through polarizers". How does that work exactly, given that the measurement must determine the direction of polarization from a single photon only?

Be careful of the term "circular polarization" and the misleading graphic in the video by PBS and O'Dowd. Circular polarization is typically just a mix of 2 linear polarizations (such as produced by certain photonics crystals) ... it can also represent a range of polarizations such as in down conversion where one set of photons is mostly to the right and the other entangled partner set mostly to the left.

Also in the video the whole concept of hidden variables is the subject of much debate. The quantum mechanical purists (those that follow strict QM rules) say nothing can be pre-determined=no hidden process, i.e only at collapse are the polarizations created. A more modern and common sense approach is that 2 photon down conversion is a specific atomic process where the opposite polarizations are set ... what is random in that we do not know if its right/left or left /right.

A polarizer just acts as a probability/angle filter and also an output filter ... i.e incoming photons at good angles have the best probability of getting thru and the output photons are all aligned like a laser outputs them.

• I thought circular polarization if a single photon was essentially the photon spin? Rather than circular being a superposition of linear polarizations, I thought it was the reverse. Commented May 10 at 19:08
• To my understanding, circular polarization is a "mix" (not quite a superposition?) of horizontal and vertical linear polarization with a phase shift of $\pm\pi/2$ between the two. Then the sign of the phase shift determines the "direction" of the circular polarization. According to this answer, one can insert a quarter-wave plate to turn circular into linear polarization (which makes sense, adding another $\pm\pi/2$ to the phase shift, resulting in $\pm\pi$ or $0$ net phase shift). Commented May 10 at 19:47
• If I understand correctly, the polarization of a single photon can never be measured, as it will either pass through the polarization filter or not. All that can be measured is the rate at which multiple similar photons will pass through the filter. Or, for the experiment, the photons are not similar as their polarization may change, but the correlation between the two photons is similar, so the measured statistic is the rate difference observed at the two polarization filters. Is my understanding correct? Commented May 10 at 19:49
• @a_guest Single photons ARE measured as to polarization. For entangled pairs, the modern method to use a Polarizing Beam Splitter (PBS) - not to be confused with a Beam Splitter (BS) which does not measure polarization. A PBS has 2 output ports (H/V) with detectors by each port that records the detection timestamp. One photon in, one and only one photon out. You can orient the PBS at any angle, so for 2 entangled photons you have 2 angles. Their difference is called Theta, and that drives the statistical prediction. To gain a fuller understanding, read: arxiv.org/abs/quant-ph/0205171 Commented May 10 at 22:50
• @RC_23 circular and spin are not related. Spin is just another way of saying polarized. The circular thing is very confusing and misleading in general. Commented May 11 at 0:36

I don't have a link to the Clauser paper, but the following from Aspect et al (1981) uses exactly the same technique. "Following Freedman and Clauser, we used the 4p''S, -4s4p... cascade in calcium (Fig. 1). This cascade yields two visible photons v1, and v2, correlated in polarization."

Experimental Tests of Realistic Local Theories via Bell's Theorem

To perform a proper Bell test, you need to use linear polarized photons (as you suggest). This was done in this experiment: "The source was run and a linear sheet polarizer was inserted in front of each polarizer." Modern Bell tests usually use polarizing beam splitters rather than polarizers, but either one can get the job done.

A linear polarizer can, of course, be oriented at any desired angle. In the ideal case, 50% of the photons would be absorbed at each side. It is the relative angle between the polarizer setting (usually called theta) that determines the quantum prediction for coincidence. Usually some form of the Clauser-Horne-Shimony-Holt inequality is used.

In general, you can convert circular polarized photons to linear polarization by inserting a quarter wave plate in the stream.

I hope this helps.

• Okay, so that means that the polarization of a single photon cannot be measured? If I understand correctly, all that can be measured is if a (linearly polarized) photon passes through a polarization filter or not but that says nothing about its polarization. Only when many photons are measured, one can derive an estimate of their polarization from the observed statistics? Then, for the experiment the correlation of these results from the two polarization filters are considered. Is my understanding correct? Commented May 10 at 19:42
• @a_guest Sorry I wasn’t more clear. Yes, individual photons are measured as to their polarization. You don’t necessarily know their polarization prior to the polarizer, you only know it after (if it was previously entangled). Entangled photons are in a superposition of polarization while entangled. Note that this is the generally accepted viewpoint, and some quantum interpretations describe things differently. But there is no question about the experimental results. Commented May 10 at 22:22
• @a_guest Also, keep in mind that the calcium cascade experiments were very early. The state of the art has radically improved in 40+ years. Entangled photons are regularly created in the undergraduate lab using Parametric Down Conversion. Times can be detected for individual photons to the picosecond level and better. Entangled pairs can be manipulated in many ways, including through fiber, filters, beam splitters, mirrors, and long distances. Commented May 10 at 22:33