# Atoms spin backward while flying along a surface

Have you ever noticed that when a car is filmed, sometimes the wheels appear to be turning backwards? For cars, having the wheels rotate in the opposite sense to the car’s motion is an artifact. But, for atoms, it may actually happen.

## Picture this

Let’s set the scene. A flat sheet of metal, hanging in the vacuum: the camera pans to see a single atom moving flat-out a few nanometers above the surface.

The electrons surrounding the nucleus of the atom push the electrons in the metal away from the metal’s surface, creating a kind of bow wave of charge in front of the nucleus and a wake of charge behind it. What we’re looking at is the very picture of a quantum salt flat racer.

The forces that generate the bow wave and wake are carried by virtual photons that are exchanged between the metal surface and the atom. In the exchange process, the atom will emit a steady stream of real photons in the direction of travel. The momentum kick from launching these photons slows the atom. This is, ultimately, friction for a single atom.

The calculation for that scenario is old and only takes into account translational motion. But, the researchers asked themselves, does the atom also rotate? More carefully put, are the forces between the surface and the atom such that they might produce a torque?

## Rotation is forbidden

The straightforward answer to this is no. Previous calculations showed that the photons emitted by the atom are linearly polarized, which means that they carry no spin momentum. That seemingly rules them out as a source of angular momentum that would spin the atom. If the atom were to start rotating, then something else has to provide the angular momentum. In the quantum world, this can only happen if electrons or photons carry away or deliver some angular momentum.

In this case, the researchers show that photons with spin angular momentum are emitted, meaning the atom has to start rotating to keep everything balanced.

But the equations also show that these photons can only be emitted opposite to the direction that the atom is traveling, which will cause the atom to accelerate. In other words, the atom doesn’t just start to rotate, it is also speeds up in the direction of its motion. Indeed, on the face of it, all friction appears to have vanished, which seemed unrealistic.

To obtain a realistic result, the researchers had to abandon the standard approach of assuming a local equilibrium between the atom, the light fields, and the plate. Instead the researchers, in their calculations, required that the velocity remain the same. For that to happen, an external force has to be applied to overcome the frictional forces.

The resulting calculation shows that the total frictional force on the atom is reduced but does not vanish entirely. This is a bit analogous to the difference between sliding and rolling friction. You can slide a tire along the road surface, but the frictional forces that resist sliding are much greater than rolling. It is kind of remarkable that the friction experienced by an atom moving close to the surface of a metal plate will also be reduced by rotating.

That, however, is nothing when you consider that the atom is rotating in the wrong direction—well, wrong compared to what we expect if it were a car tire. Imagine, if you would, that the tires on your car were spinning backwards, but the car proceeded forward quite happily.

## Rubidium racers

To make their calculations a little more concrete, the researchers identified the forces and accelerations for specific combinations of atoms and metal surfaces. They found that, for a rubidium atom flying across a gold surface at 30km/s, the frictional forces result in 30nm/s2 deceleration. That is pretty close to the limits of our current ability to measure acceleration in single atoms. On the other hand, a lithium atom flying across a sodium surface at 10km/s will experience a deceleration of 2.5µm/s2, which should be measurable (even if creating a flat surface of sodium is difficult).

In the end, directly measuring the atomic rotation may be easier. The rotating atom has to emit photons with a frequency that corresponds to the speed of rotation, which is about 25MHz (e.g, below FM radio frequencies). Single photons at 25MHz are hard to detect, but a steady stream of atoms might emit enough radiation to let us pick it up.

Assuming that the calculations and later experiments work out, I still don’t know what these results mean. The concept of an atom rotating is very fuzzy and ill-defined. It is not like the electrons are in planetary orbits and a very tiny cat is upending a tiny solar system. Some electrons have spherical orbits, meaning rotation does not change anything. Other electron orbitals have a defined orientation but only relative to each other. Then, of course, there is the nucleus. Is that rotating, too?

## Dumbbells

After giving it some thought, I think rotation only has meaning in the following way. Some electrons are stored in atomic orbitals that look a bit like dumbbells that are at right angles to each other. If all of those orbitals are filled with electrons, then rotation makes no sense, because the atom is symmetric and rotation is effectively swapping the orbital labels for each electron—nothing really moves. Even if the orbitals are distorted by the surface and have different energies, the electrons just swap energy with each other as well.

However, if an atom only has a single electron in one of the dumbbell orbitals, then the label swapping trick might not work and there are no electrons to exchange energy with. As the orbital swings around in space, the electron might gain energy as it approaches the surface and give the energy up as a photon as it jumps to the next dumbbell orbital. That, conceptually at least, seems a lot like rotation.

Physical Review Letters, 2019, DOI: 10.1103/PhysRevLett.123.120401 (About DOIs)