  Free electrons are essential in such diverse applications as electron
microscopes, accelerators, and photo-emission spectroscopy. Often, space charge
effects of many electrons are a nuisance. Confined to extremely small
space-time dimensions, even two electrons can interact strongly. In this case,
the Coulomb repulsion can now be highly advantageous, because it leads to
surprisingly powerful electron-electron correlations, as we demonstrate here.
We show that femtosecond laser-emitted electrons from nanometric needle tips
are highly anti-correlated in energy because of dynamic Coulomb repulsion, with
a visibility of $56\,\%$. We extract a mean energy splitting of $3.3\,$eV and a
correlation decay time of $82\,$fs. Importantly, the energy-filtered electrons
display a sub-Poissonian number distribution with a second order correlation
function as small as $g^{(2)} = 0.34$, implying that shot noise-reduced pulsed
electron beams can be realized based on simple energy filtering. Even heralded
electrons could become available for quantum-enhanced electron imaging
protocols. Furthermore, we also reach the strong-field regime of laser-driven
electron emission. We gain deep insights into how the electron correlations of
the different electron classes (direct vs. rescattered) are influenced by the
strong laser fields. Our work levels the field of quantum electron optics, with
direct ramifications for shot noise-reduced and quantum electron imaging as
well as direct measurements of correlated electrons from inside of strongly
correlated matter.
