If you shine a beam of light from a laser or flashlight, the beam will spread out over distance, becoming wider and less intense far from the source. That phenomenon is called diffraction, and it is one of the fundamental aspects of the wave nature of light. But, in 2007, researchers overcame that limit, and created curved beams of light that did not diffract by carefully shaping their waveform.

Now an experiment has used electrons' wave properties to create similar curved beams of electrons. Noa Voloch-Bloch, Yossi Lereah, Yigal Lilach, Avraham Gover, and Ady Arie sent electrons through a holographic film, which shaped their wave characteristics the same way that earlier experiments did for light. Without any additional force, the electrons followed parabolic trajectories while remaining in a tight beam. These paths even "healed" after passing obstacles, restoring their shape as though the objects were not there.

According to quantum physics, particles and waves are two aspects of the same system. The trajectory of a particle is actually governed by its quantum-mechanical wave function, which gives the probability for a particle may be found at a particular position. Waves traveling through an aperture, for example, will interfere with themselves, producing a gradually spreading beam where the particles follow diverging paths; that's diffraction. Lasers, flashlights, and the like send light through an opening, and so all they experience diffraction.

Creating curved trajectories—known as Airy beams—is a matter of manipulating the quantum wave function. In an Airy beam, waves interfere in a way that ensures particles are most likely to trace parabolic trajectories rather than straight lines. Because the entire wave function behaves differently than it does under ordinary circumstances, the particles no longer diffract—meaning Airy beams also maintain their intensity over large distances.

Dodging Isaac Newton

In Newton's laws of motion, a particle will travel in a straight line at a steady speed unless an external force acts on it; you need a constant net external force to produce parabolic trajectories from Newtonian perspective. In quantum physics, the wave function still obeys a form of Newton's laws. The statistical average of a wave function (its centroid) still tracks a straight line when there is no external force. The key thing is that the probability of finding a particle at a given position may not follow the same line.



Electrons also experience diffraction and interference, which is the source of the famous quantum double-slit experiment. In the new experiment, the researchers manipulated the wave function of an electron beam by sending it through a specific holographic pattern. They focused the beam using a magnetic field that acted much like a lens, producing a distinctive triangular bundle of electron beams. Each bundle followed a curved path, which the researchers determined by measuring the electron patterns at various distances from the hologram.

One strange consequence of Airy beams is their ability to self-heal. When the electron Airy beam reached a glass wire that partly blocked its path, the trajectories compensated for the barrier, ultimately producing exactly the same pattern with or without the obstacle in place.

Previous research on Airy beams of light has shown they can be shaped in a number of arbitrary ways, and maintain their coherence over large distances. The new results suggest the same thing is true for electrons. Shaped, diffraction-free electron beams would be extremely useful in tunneling electron microscopes (TEMs), commonly used to manipulate and image the surface properties of materials. Long-range coherent beams would also be handy for studying the properties of the electrons themselves, including their interactions within atoms.

Nature, 2013. DOI: 10.1038/nature11840 (About DOIs).