Abstract

The recent development of on-demand semiconductor single-electron sources such as mesoscopic capacitors [1] and leviton excitations [2] has enabled an electronic analogy of quantum optics experiments. This allows the detailed studies of electron emission dynamics [1], fermion quantum statistics [2,3], and the roles of electron-electron interactions [4,5] in electron transport using shot-noise [2,3,5] or ac-current [1,4] measurements. However, some of the electron dynamics occur at such short timescales that they are inaccessible by the bandwidth of conventional measurement techniques. We demonstrate an experimental method to detect electron arrival-time distribution with resolutions as small as 1 ps, and show that this technique can be used to study the details of electron dynamics in quantum-Hall edge-state transport. Our electrons are emitted from a GaAs quantum-dot pump as hot electrons at energies ~100 meV above the Fermi energy [6]. These electrons travel through quantum-Hall edge states acting as electron waveguides. A fast-rising detector potential barrier, driven by an rf signal synchronised to the pump, acts as a shutter for incoming electrons. The measurements of transmitted electron current provides the information on the arrival-time distribution as the time delay of detector barrier rise is shifted against the timing of electron emission [6,7]. We have detected electron arrival-time distribution as small as 4 ps. We use this technique to perform time-of-flight measurements to deduce edge-state velocity [8]. Our results agree with the E ⃗×B ⃗ drift model, where the electron drift velocity is inversely proportional to the applied magnetic field. By measuring the energy dependence of velocity, we estimate the edge-confinement potential profile, created by the combination of a chemically-etched mesa and a voltage applied to the surface gate that covers the edge. The same time-of-flight technique is used to deduce inelastic scattering rates due to LO phonon emission. We compare these experimental results against a theory based on Fermi’s-golden-rule calculation [9].

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