What Happens When You Cut a Photon in Half?

A photon is a single particle of light, and under normal circumstances, it can’t be divided. But a photon is also not a particle, in the sense that it does not have a specific location. Instead, it is an extended object.

So if a photon is only partway through the process of reflecting from a perfect mirror and you yank the mirror away, what happens? The answer, from a trio of Norwegian physicists, turns out (arxiv.org link) to be more complex than I expected.

A photon divided?

Let’s first talk briefly about dividing and combining photons. If this were a common experience in our lives, then shining a single color of light through a piece of glass or reflecting it from a surface might cause photons to divide or combine. This would lead to an amazing array of colors: Our universe would be the most fantastic and legal LSD trip you could imagine. But this doesn’t generally happen, hence LSD.

What does happen is that photons can divide and combine under the right circumstances—essentially, the medium through which the light travels has to change in response to the light. This can lead to a rainbow of colors from a single color source.

Technically, we would say that the light interactions we see around us are linear, and the combination/division of photons is a nonlinear process. Typically, to overcome that nonlinearity, you need either a very sensitive medium or a very high-intensity light source, like a laser.

The sudden removal of the mirror while a photon is reflecting is not nonlinear in the way that I would normally think about it. But if you give it more than a moment’s thought, it’s clearly a nonlinear event. This line of thinking is obscured by how we think about single photons at mirrors, though, as I will illustrate below.

A single photon goes through the looking glass

Or does it?

Let’s start with the example of a partially reflective mirror. When a single photon hits that mirror, it will either go through the mirror or reflect from the mirror. The photon is considered to enter a superposition state of having both reflected and passed through (the probabilities of each path depending on how reflective the mirror is). If we place detectors in the path of the reflected and transmitted photons, when one clicks, it collapses the superposition, and the other potential path disappears.

There are no circumstances in which both detectors will click at the same time. We do not record half a photon each way.

Naively, we could make the same argument for a fully reflective mirror that is removed midway through reflection. In this argument, the photon enters a superposition state of transmitted and reflected, with the probability determined by when the mirror was removed compared to the “size” of the photon. Again, when we try to measure which way the photon went, we’d expect the superposition to collapse, and only one detector would click.

But that is not what happens.

When I stopped to think about it, it was obvious that this was wrong. But to understand why, we need some extra theoretical baggage.

A photonic thunderclap

Time and frequency are two sides of the same coin. If we play a note on a piano, there is a time-domain picture: a regular variation in pressure with time that continues for quite a while. This note can be described by a single frequency with a single amplitude (how loud it is). More complicated sounds (chords, staccato notes) have a complicated structure in time and are described by more complicated combinations of frequencies, each with its own amplitude (phase also matters, but we will ignore that).

This picture is universal and applies to all time-varying signals—and far more than those, too. When I was growing up on the farm, listening to AM radio on an old-fashioned (even then) tube radio, the music was always interrupted by a clicking noise. The clicking was from our electric fence, which was always zapping some errant grass, a misbehaving sheep, or a horny bull.

That short-sharp current generated a short electromagnetic pulse (and an angry bull). The very short pulse (in time) was present across a very broad spectrum, including, to my annoyance, the AM broadcast spectrum. The shorter an event in time, the more frequency spectrum is required to support it. On the flipside, a single tone that does not change for a very long time requires very little spectrum (only the tone itself).

This rule also applies to photons reflecting from mirrors. The photon is reflecting from the mirror, and the electromagnetic field is varying regularly and smoothly changing from the incoming to the reflected wave. The transmitted wave doesn’t exist, so the amplitude is a happy zero.

Then the mirror is yanked away. The reflected wave’s amplitude abruptly drops to zero, and the transmitted wave suddenly jumps from zero. Those are two sharp transitions that require a lot more bandwidth than the original photon had. Our photon that has been cut off is still in a superposition of reflected and transmitted. But it also has a sharp edge, which requires a multitude of photons at different frequencies.

Cutting a photon in half generates a rainbow. And as far as I can tell, the generated photons are in a superposition of both reflected and transmitted light. But since there are potentially many photons, both transmitted and reflected light could be measured simultaneously.

Can we do it for real?

This will be a complex experiment to perform. Researchers will need a source that generates single photons on demand with a very narrow spectral bandwidth. This will spread them out in time so that any additional photons that come from cutting it off are observable. They then need to be able to trigger the mirror at the right time.

This won’t be done with something like a bathroom mirror. The authors calculate that the transition from reflective to transmission needs to take place in about 10 femtoseconds (a femtosecond is 10-15 s), which is insufficient time to move a physical mirror. Some materials, like semiconductors, can be driven from reflective to transmission quite rapidly (30-100 fs) using ultrafast laser pulses as the switch. Unfortunately, that laser pulse gets in the way. It will be quite difficult to filter out the big laser pulse used to remove the mirror so that the photons generated by cutting the long single photon are observable though.

We already have some evidence that this works, though. The mirrors I described above are used to shorten ultrashort pulses, which means that the reflected pulses have more frequencies after reflection, and new photons must therefore be generated. We just haven’t observed it for single photons yet. But give it about a year, and I’d bet we will.