As Above, So Below: Asteroid Motion on an Atomic Scale

Physics stories often highlight the strangeness of the quantum realm in comparison to our everyday world, the difference between what we experience and what happens at the nano-scale. Sometimes, though, you can gain more insight by focusing on the similarities between two situations than on their differences.

That’s the case in new research that draws on the classical description of an asteroid orbiting the Earth to better understand a complicated quantum system. The work was recently published in the American Physical Society’s journal Physical Review Letters by a team of scientists from Aix-Marseille Université, the French National Center for Scientific Research (CNRS), and the Georgia Institute of Technology.

(Click to enlarge)
An illustration comparing the motion of an asteroid under the influence of the Earth’s gravity to the motion of an electron under the influence of an ionized molecule’s electrostatic field.
Image Credit: Jonathan Dubois.

In the growing field of attophysics—“atto” refers to a billionth of a billionth–researchers use attosecond bursts of electrons or photons to study matter. At this time resolution, its possible to probe the electronic structure of matter and even watch molecular interactions taking place. It’s opening up new avenues to explore things like the biochemical processes that take place inside the human body.

One of the best ways to see these processes in action is through recollision experiments. When you illuminate a molecule with a laser pulse under the right conditions, an electron can escape. That electron will feel two forces—one from the laser and one from the now positively charged molecule. “These two forces are in competition with each other,” explains lead author Jonathan Dubois, a doctoral student at Aix-Marseille Université.

Under these two forces, the electron travels freely for a while. Then, the laser pushes it back home on a collision course with the molecule, with two possible outcomes depending on the molecule’s structure: the molecule can either recapture or scatter the electron. So, by performing recollision experiments in quick succession and analyzing the results (like the direction and momentum of scattered electrons), you can get a picture of the molecule’s structure as it changes in time.

Here’s the problem. The electron’s trajectory doesn’t just depend on the structure of the molecule, it’s also influenced by the electrostatic field of the molecule and the laser field. That means that in order to get a clear picture of the structure of the molecule, you need to subtract the influence of these fields on the electron’s motion. That’s not an easy task.

The path of an electron in this situation isn’t just hard to predict, it’s mathematically unsolvable. In other words, there’s no way through the problem—you have to go around it. Most of the time, says Dubois, researchers do this by focusing on the influence of the laser field and ignoring the electrostatic field, or by treating it as a perturbation to the laser field. That works for some situations but not all.

Inspired to find a better way, the team realized it might be possible to separate the influence of the two fields using a mathematical technique commonly used by astronomers. Despite the vastly different scales and contexts, the equations that describe the motion of the electron in the molecule’s electrostatic field turn out to be very similar to the ones that describe the motion of an asteroid in Earth’s gravitational field.

The researchers set up a simplified model of the electron’s situation that exploits this similarity and also includes the force of the laser field. Their work reveals that the electron orbits around a kind of “guiding center.” This guiding center is the average path of the electron, as determined by the electrostatic field, and the laser field drives the electron’s motion around that guiding center.

It’s an interesting model, but is it useful? That wasn’t clear at first, says Dubois, but after a few months they put it to the test. A 2013 recollision experiment in Ursula Keller’s lab at ETH Zurich had yielded results that didn’t match predictions made with previous models—the data included features that couldn’t be explained.

When the team put these experimental conditions into their asteroid-inspired model, the resulting predictions contained the same features observed by the ETH group. Then, by analyzing the electron trajectories produced by the model, the team discovered the physical reason behind the features: Put simply, the electrostatic field couldn’t be ignored. Now, thanks to this work, it doesn’t need to be.

As we strive to better understand the motion of electrons, the structure of matter, biomolecular interactions, and the world in general, it’s worth remembering that insight can come from appreciating similarities as well as differences, even across vastly different scales. Sometimes, applying a familiar tool to a strange situation can be just what you need to see the picture more clearly.

Kendra Redmond

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