Superoscillating electron wave functions with subdiffraction spots

Abstract

Almost one and a half centuries ago, Abbe [Arch. Mikrosk. Anat. 9, 413 (1873)] and shortly after Lord Rayleigh [Philos. Mag. Ser. 5 8, 261 (1879)] showed that, when an optical lens is illuminated by a plane wave, a diffraction-limited spot with radius $0.61\ensuremath{\lambda}/sin\ensuremath{\alpha}$ is obtained, where $\ensuremath{\lambda}$ is the wavelength and $\ensuremath{\alpha}$ is the semiangle of the beam's convergence cone. However, spots with much smaller features can be obtained at the focal plane when the lens is illuminated by an appropriately structured beam. Whereas this concept is known for light beams, here, we show how to realize it for a massive-particle wave function, namely, a free electron. We experimentally demonstrate an electron central spot of radius 106 pm, which is more than two times smaller than the diffraction limit of the experimental setup used. In addition, we demonstrate that this central spot can be structured by adding orbital angular momentum to it. The resulting superoscillating vortex beam has a smaller dark core with respect to a regular vortex beam. This family of electron beams having hot spots with arbitrarily small features and tailored structures could be useful for studying electron-matter interactions with subatomic resolution.