Few-electron correlations after ultrafast photoemission from nanometric needle tips

Abstract: 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.