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Characterizing distinct electron wave packets is a basic task for solid-stateelectron quantum optics with applications in quantum metrology and sensing. Aimportant circuit element for this task is a non-stationary potential barrierthan enables backscattering of chiral particles depending on their energy andtime of arrival. Here we solve the quantum mechanical problem ofsingle-particle scattering by a ballistic constriction in an fully depletedquantum Hall system under spatially uniform but time-dependent electrostaticpotential modulation. The result describes electrons distributed in time-energyspace according to a modified Wigner quasiprobability distribution andscattered with an energy-dependent transmission probability that characterizesconstriction in the absence of modulation. Modification of the incoming Wignerdistribution due to external time-dependent potential simplifies in case oflinear time-dependence and admits semiclassical interpretation. Our resultssupport a recently proposed and implemented method for measuring time andenergy distribution of solitary electrons as a quantum tomography technique,and offer new paths for experimental exploration of on-demand sources ofcoherent electrons.

Time-energy filtering of single electrons in ballistic waveguides