Quantum Tomography of Solitary Electrons

Initializing and measuring the wave-function of single freely-propagating particles are challenging but fundamental tasks for applications in quantum information processing and enhanced sensing. Recently, continuous-variable quantum tomography techniques developed for atomic beams and photonic modes have been adapted for on-demand electronic excitations but are limited to the region in energy-time phase space immediately around the Fermi level. Here we present a general, broad-band method for mapping the single-particle phase space Wigner distribution. We reconstruct the Wigner representation of the mixed-state density matrix for \textit{solitary} electrons emitted by an on-demand source. This reveals highly localised distributions isolated from the Fermi sea. Our method can be used to test the degree of `quantumness' of an electron source from measurements of the phase-space density. While both source purity and detector fidelity are suppressed by classical fluctuations, here we resolve fine structure of the wavepackets (a chirp controlled by emission conditions) and find that the resolution should be sufficient to enable quantum-limited measurements. Our technique will provide key information required to master electron coherence and entanglement at the individual particle level, for instance to create excitations from multiple sources that are indistinguishable.