Fig. 1: Principle of the experiment.

a, QPC A and QPC B are used for partitioning of the outer-edge channel with transmission probabilities T_i = 1 − R_i (i = 1, 2), defining an electronic FPI. A single-electron pulse V_pulse(t) is sent through the bottom-right branch of the interferometer. The square voltage \({V}_{{\rm{G}}}^{\rm{a.c.}}(t)\) we probe is imposed on the central gate located on the upper arm of the FPI. The d.c. current I_out is measured at the output of the FPI (bottom left). b, False-colour electron microscopy image of the sample. QPCs A and B are indicated in yellow. The interferometer is an FPI of height H = 2 ± 0.2 μm (taking into account a depletion length of 0.25 ± 0.1 μm on each side of the sample) and width W = 3.6 ± 0.2 μm. The perimeter of the FPI is L = 2 × (H + W) = 11.2 ± 0.8 μm and its area is A = 7.2 ± 0.8 μm². The excitation gate (red) is connected through a bias-tee to a d.c. and a.c. source such that we can send both radio-frequency square excitation \({V}_{G}^{\rm{a.c.}}(t)\) and d.c. voltage \({V}_{\rm{G}}^{\rm{d.c.}}\). A magnetic field \({\bf{B}}\) perpendicular to the surface is applied to the sample. The two-dimensional electron gas mesa is indicated in blue and ohmic contacts are indicated in purple. All the other gates (grey) are not used in this experiment and are left floating. c, V_pulse(t) is a single-electron Lorentzian pulse of width τ_e. The square voltage \({V}_{G}^{\rm{a.c.}}(t)\) has a width τ_s and a peak-to-peak amplitude \({V}_{G}^{\rm{a.c.}}\). t₀ is the time delay between \({V}_{G}^{\rm{a.c.}}(t)\) and V_pulse(t). d, In the HOM configuration, we probe the width of the Lorentzian pulses by measuring the current noise coming out of QPC A. e, Result of the HOM experiment showing the amplitude of noise (dots) as a function of the time difference between the two incoming Lorentzian pulses on QPC A for τ_AWG = 16 ps (blue) and τ_AWG = 47 ps (orange). The error bars represent the standard error of the noise measurements and are centred around its mean value. A fit of the data (in dotted lines) shows that the actual time widths at the level of the sample are 35 ps and 63 ps. f, Measured width of the pulses as a function of the set time on the AWG for pulses containing one (1e; red) or two (2e; purple) electrons. We observe a linear dependence of τ_e = τ_AWG + 20 ps. The error bars are extracted from a Lorentzian fit of the HOM noise data and represent one standard deviation (as shown in e).