  We demonstrate the generation of Coulomb-correlated pair, triple and
quadruple states of free electrons by femtosecond photoemission from a
nanoscale field emitter inside a transmission electron microscope. Event-based
electron spectroscopy allows a spatial and spectral characterization of the
electron ensemble emitted by each laser pulse. We identify distinctive energy
and momentum correlations arising from acceleration-enhanced interparticle
energy exchange, revealing strong few-body Coulomb interactions at an energy
scale of about two electronvolts. State-sorted beam caustics show a discrete
increase in virtual source size and longitudinal source shift for few-electron
states, associated with transverse momentum correlations. We observe
field-controllable electron antibunching, attributed primarily to transverse
Coulomb deflection. The pronounced spatial and spectral characteristics of
these electron number states allow filtering schemes that control the
statistical distribution of the pulse charge. In this way, the fraction of
specific few-electron states can be actively suppressed or enhanced,
facilitating the preparation of highly non-Poissonian electron beams for
microscopy and lithography, including future heralding schemes and correlated
multi-electron probing.
