# Slowing Down (and Speeding Up?) a Beam of Light

Q:
Based on the recent experiment where a photon was permanently slowed down by changing it's shape, is it possible that we could somehow increase the speed of the photon to past the speed of light by changing it's shape?
- Charles Allard (age 18)
Beeville, TX, USA
A:

The experiment you mention is described in a recent . Because many readers won't have access to the original paper, here's a  about the experiment.

Changing the "shape" of a photon really means we're changing its "spatial mode" or the shape of the beam it's in. If you shine a laser pointer on the wall, its shape is usually close to a Gaussian beam, like . There are other kinds of beams, such as  and, with different shapes. The shape of the beam is determined by interference between waves traveling in slightly different directions.

It's these slightly different directions that make some beams travel slower than others. I tried to show how this works for a Bessel beam (which is what the authors of the recent paper used in their experiment) in the picture below. Warning: this explanation is going to get long, but it will end with something very simple. Light can act like a wave. In the picture, the solid blue lines are the peaks of that wave, and the empty spaces between them are troughs. On the left is a "plane wave": all the peaks line up with each other across the beam. The momentum of the beam is shown with a red arrow, and the length of the arrow represents the magnitude of the momentum.

Now the plane wave passes through an axicon, a sloped piece of glass that transforms the light into two plane waves traveling in slightly different directions. Where the two waves overlap, they interfere: if two peaks or two troughs coincide, that produces a bright area (constructive interference), but a peak and a trough will cancel and produce darkness (destructive interference). A unique property of a Bessel beam is that it has a band of constructive interference at its center, which forms a beam that doesn't spread out much as it travels. This is shown in green in the picture. (Bessel beams are really cool; you can read more about them .)

Since the two plane waves are now traveling in different directions, they have different momenta. The momentum of each plane wave is again represented with a solid red arrow. Each arrow is half the length of the original one, because the two plane waves each (sort of) have half of the original number of photons.

The dashed red arrows show how much of that momentum is directed along the beam, and how much is perpendicular to the beam. The parts (or components) of the two momenta that are perpendicular to the beam point in opposite directions, so they cancel each other out. The parts that are along the beam point in the same direction, so they add. The two dotted red arrows in the center of the beam show the total momentum when the two plane waves are combined. Notice that the length of those two arrows together is less than the original momentum arrow. The Bessel beam has less momentum along the beam than the plane wave does, because some of its momentum was directed perpendicular to the beam.

Just to emphasize how simple this really is: for exactly the same reason, you should run a race straight towards the finish line instead of at an angle. If you run at an angle, some of your momentum is "wasted" because it's directed perpendicular to the finish line instead of towards it.

It's a bit complicated to explain how this momentum along the beam is related to the speed of light—but basically, as the momentum in the direction of the beam gets smaller, the "group velocity" of the light gets slower. This is the speed at which any information carried by the light would travel. The authors of the recent paper compared a Bessel beam with a plane wave very precisely and found that the Bessel photons did take slightly longer to travel the same distance. However, there's no way to rearrange the momentum of the beam so that the group velocity is faster than the speed of light, just like there's no way to run a race faster than straight towards the finish line.

Rebecca Holmes

PS: One more thing about this experiment: this effect has actually been known for a long time, but had only been demonstrated for classical beams of light such as lasers. It was predicted that single photons should behave the same way, and the authors of this study were the first to do an experiment that proved it.

The fact that this works for single photons illustrates something very strange about quantum mechanics. It's easy to understand a Bessel beam if we think about classical plane waves. But a single photon can also have all the properties of a beam of light. It travels in a superposition of all the possible momentum directions in the beam, and it interferes with and combines momentum with itself.

(published on 02/10/2015)

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