A surfer glides across the ocean surface until a big wave comes, and then they're flying forward. Similarly, a free electron interacts with light: usually the energy exchange is barely noticeable, but if the surrounding medium begins to oscillate rhythmically, each wave crest pushes the particle harder and harder.
The authors considered the quantum interaction of electrons and photons in a medium whose properties oscillate periodically. It turns out that such modulation creates band gaps in momentum space — intervals where energy cannot change smoothly. At the boundaries of these gaps, the coupling between the electron and light grows avalanche-like. This allows transferring a huge momentum to the particle, much larger than under ordinary conditions.
The result is controlled growth of the electron's energy without bulky magnetic fields. Instead of multi-kilometer accelerators — a thin slab with a traveling light wave. The surfer catches not just one wave but a whole series, and each adds speed. Thus, time-modulated photonic media become a platform for particle acceleration and sculpting their quantum states.
The idea of particle acceleration in periodic structures dates back to post-war linear accelerators, where electrons were accelerated in a chain of resonators. The new method replaces metal cavities with a light wave on a tiny chip.
In Charles Stross's novel 'Accelerando', posthumans use light sails for interstellar travel — here the same principle works at the quantum level for individual particles.