Researchers: Forget old experiments, let’s reinvent the wheel

One of the joys of the arXiv is that anyone can submit anything to the website. Cranks and kooks can publish to their hearts' content in the theoretical physics section. Their work will remain there, read only by those searching for casual amusement. Yet somewhere between all the excellent science and slapstick comedy are scientists who just get stuff flat out wrong.

This is the story of how two respected physicists failed to understand photon angular momentum. Don't worry, they're not alone. Every physicist who has given the subject any thought has lost sleep working it out (and has had nightmares involving Jackson's Classical Electrodynamics). Since I lost sleep over it, I figured I would ensure that you all lose some sleep too.

Spinning photons and rotating electric fields

The fundamental confusion arises from the fact that there are two equivalent ways of describing the angular momentum of a photon. A cursory inspection of nature, however, seems to reveal that one is more natural than the other.

A photon's angular momentum can generally only take on two values: +1, and -1. These values tell us about the behavior (or polarization) of the electric field of the photon. Imagine that you're standing in the path of a stream of single photons and that you can see the electric field of each photon as it passes by. For some photons, the electric field rotates like the hand on a clock: these photons have an angular momentum of +1, termed "right circular polarization." For others, the direction of rotation is reversed—"left circular polarized," or an angular momentum of -1.

This all seems pretty straightforward until you realize that if you set your light source to emit a left circular polarized photon and a right circular polarized photon at the same time, you will observe a linearly polarized electric field. Likewise, two linearly polarized light fields, with the right orientation and timing, give us a circularly polarized electric field. This is where the confusion arises: might a single linearly polarized photon always actually be a pair of circularly polarized photons?

The two descriptions are mathematically equivalent. Classical electromagnetism—for which the photon doesn't exist—doesn't care, and you should use whichever polarizations are most convenient to understand the physics. But at the lowest possible light intensities, where you would expect to detect just a single photon at a time, it matters. Where we think we have a single photon, we actually might have two.

Nature: It likes to spin

Does nature prefer its photons to have angular momentum? A cursory inspection suggests it does. The individual photon always has a spin, and we can see this in the behavior of atoms. If an atom is put in an excited state, it will emit a photon, and that photon will have angular momentum, which seems obvious.

But, where does that angular momentum come from? In an atom, the electrons are arranged in orbitals that have a specific geometric shape. So S shells are circular, while P shells look a bit like dumbbells. An electron in one of these shells is not a particle zipping around like some demented fruit fly. It's a wave, spread out through the shell. The shape of the shell determines the angular momentum. For instance, an S shell electron is made up of many component waves that travel in circles.

Now imagine that you are an electron in an S shell and you want to emit a photon to lose some energy. You can't emit anything but circularly polarized light, since the waves that determine your momentum and position are traveling in circles. You also can't go to another, lower energy S shell, because you no longer have the right angular momentum. Instead, you must go to a P shell. So conservation of angular momentum tells us a lot about what light an atom will and will not emit.

What we find is that single atoms always emit circularly polarized light so that the electrons have the right angular momentum for the shell they are about to enter. If we limit ourselves to atoms and molecules, we would conclude that nature loves its circular polarized photons.

But a free electron is under no such restrictions. For instance, if we pass a single electron through a pair of magnets that make it wiggle like a snake, the electron will emit a single, linearly polarized photon for each wiggle. (The photon's wavelength is given by the electron energy and the magnets' separation.) Similarly, electrons confined in long, narrow boxes will emit linearly polarized light. So although nature seems to construct entities that prefer to emit circularly polarized light, circularly polarized light does not have some hierarchical preference.

But, we know that a photon has to have spin, so how can a single linearly polarized photon exist? Well, in this case, the single photon is in a superposition state of +1 and -1 spin states, and it behaves like it has a spin of zero. Therefore, single photons with linear polarization exist in the sense that one photon can have two spin states at the same time.

Why do we care?

All of those arguments, though, are largely theoretical in nature. If nature really didn't like single photons having linear polarization, would it matter? Yes, it would. A lot.

In quantum optics, many experiments on entangled photon pairs have relied on measuring single photons, and almost every single experiment uses linearly polarized photons. If those experiments were actually detecting photon pairs, they would be invalid. All statements about the nature of locality and realism, which were based on experimental results, would be called into question. It would be shocking. Could physicists really have made such a basic mistake?

This is where the major disconnect between our intrepid physicists and the rest of the quantum optics community appears largest. The authors have a background in superconducting devices. One of the coolest developments in recent years has been the development of photon-counting detectors based on superconducting devices. Essentially, these devices act as tiny thermometers. Every time a photon is absorbed, the temperature goes up slightly, and that uptick is measured as a change in current.

These current changes are large enough to detect single photons. But unlike traditional photon detectors, the response is linear, so two photons produce twice the current that one photon does, etc.

Using these detectors, the researchers argue, this question could be put to rest immediately.

A couple of decades late

Unfortunately, the researchers are a bit late with their suggestion. We already know that linearly polarized single photons exist. When the original experiments on locality were performed, this was a critical point. Physicists had to know that they were playing with single photons. At the time, this wasn't easy; their detectors could only distinguish between light and dark, but not between one photon or two (or three, etc.). One photon or many photons, the response from the detector was a simple click.

But using a pair of these detectors, it's fairly simple to determine if a photon stream consists of single separated photons or bunches of photons traveling together. Quite simply, you place a partially reflecting mirror in the path. When a photon encounters that mirror, it has a 50 percent chance of passing through to hit one detector or reflecting off the mirror to hit the other detector. If there is only one photon incident at a time, only one detector will click at any given time. If there are two photons, half of the time each would hit the mirror and go down a different path, so both detectors will click at the same time.

If our linearly polarized photon was really constructed of two circularly polarized photons (as opposed to a single photon in a superposition state), this would immediately show up. So, yes, we really do know that single photons can be linearly polarized. I have yet to see a paper that relied on single photon sources to not produce or reference experimental data that proves that their photon source does actually produce single photons. And they all use this experimental procedure to show it.

We know our classical intuition can't be correct, but understanding that concept is difficult. To give an example, there is an optical element called a quarter-wave plate that converts light between linear and circular polarizations. At the single photon level, the reasoning used by the researchers here suggests that this piece of crystalline material could magically generate an additional photon. To make matters worse, what works at the single photon level has to work at all intensities, so my five watts of circularly polarized light should become 10 watts simply by sending it through a thin piece of quartz.

Conservation of energy: it must be obeyed. You have to wonder what they were thinking.

ArXiV.org, 2014, Abstract number: 1407.2605  (About the arXiv).