Spatial and energetic correlations of ultrashort two electron pulses
When two electrons are emitted from a metallic needle tip into a nanometric volume on femtosecond timescales, strong Coulomb correlations arise. While longitudinal correlations, manifested as energy shifts, have been observed both from bare tips and in electron microscopes, transverse correlations remain hardly explored. Here, we present the first complete experimental characterization of such 3D correlations from needle tips. We find that electron pairs of small transversal spatial separation exhibit a pronounced energy gap of 3.3 eV width, while electrons of small longitudinal energy separation show strong transverse repulsion, increasing their average mutual divergence angle by a substantial 34.5%. The measurements are in excellent agreement with semiclassical point-particle simulations. These reveal that the maximal energy-gap magnitude is primarily determined by the laser pulse duration, whereas the maximal spatial separation is governed by the tip radius. The latter can be exploited in a remarkably simple method to generate strongly sub-Poissonian electron beams: A mere aperture, notably present in most electron-optical setups anyway, can act as an electron number sensitive filter. In combination with energy filtering we find an unprecedented suppression of multi-electron pulses reaching g(2) = 0.02 when keeping 3% of the electron beam. These results provide a foundation for future studies of electron entanglement, correlated electron microscopy, and the design of ultrafast electron-optical instruments.