A laser beam is like a swift vortex that briefly captures a passing electron. As the particle moves through the pulse, its spin (the intrinsic rotation, like a tiny top) experiences a weak kick. After leaving the beam, the top no longer points in the same direction; it has turned a little.
The effect arises because the electron has a tiny magnetic anomaly — a deviation from "normal" magnetic behavior, known as the anomalous magnetic moment. It is through this anomaly that light transfers its rotation to the particle. The magnitude of the rotation depends on the area traced out by the transverse electric field of the pulse. The more twisted the light, the larger the area and the more noticeable the effect. The area itself turns out to equal the spin angular momentum carried by the pulse per unit area, so the spin rotation directly measures the helicity (twist) of the laser beam.
The authors tested their calculations across many configurations of laser pulses. They found that if the beam is weakly focused, the effect is vanishingly small. But with strong focusing, when the light spot is comparable to the wavelength, the rotation becomes noticeable. This opens the way to experiments where the electron spin acts as an ultra-sensitive sensor of light's twist.
The electron's anomalous magnetic moment is one of the most precisely measured quantities in physics. It agrees with theory to the twelfth decimal place, and it is this tiny addition that is responsible for the spin rotation in the experiment.