Time-resolved measurement of single electrons using a modulated barrier

Measuring the wave packet of high-energy electrons in solid-state devices is important for quantum information processing. Time-resolved measurements with high time resolutions and small errors typically require detectors with a large RF bandwidth. Here, we demonstrate a precise and time-efficient time-resolved method, where an accuracy in measurements are not limited by the bandwidth. By analyzing the energy variance derived from transconductance measurements under a sinusoidal gate voltage applied to a detector barrier, we extract key characteristics of single-electron states. It includes a temporal variance and the covariance between energy and time. The results are consistent with those obtained using a hyperbolic tangent shaped (linearly varying) gate voltage. The proposed approach provides a simple yet precise method for probing the single-electron states. The present findings will be useful for identifying suitable waveforms for applications in electron quantum optics and quantum information processing.