Clock-Controlled Emission of Single-Electron Wave Packets in a Solid-State Circuit

We demonstrate the energy- and time-resolved detection of single-electron wave packets from a clock-controlled source transmitted through a high-energy quantum Hall edge channel. A quantum dot source is loaded with single electrons which are then emitted $\sim 150\mathrm{meV}$ above the Fermi energy. The energy spectroscopy of emitted electrons indicates that at high magnetic field these electrons can be transported over several microns without inelastic electron-electron or electron-phonon scattering. Using a time-resolved spectroscopic technique, we deduce the wave packet size at picosecond resolution. We also show how this technique can be used to switch individual electrons into different electron waveguides (edge channels).

Figure 1

(a) Schematic view of single electron pump and energy detector. Electrons are pumped from left to right where they are transmitted or deflected. Pump, collector and side channel currents ($I_p$, $I_c$ and $I_s$) are measured with ammeters. A signal generator operates the pump and the detector barrier via a time delay, $t_d+\Delta t_d$ and attenuator $A_d$. (b) Potential profile of pump (left) and detector (right). The deflection of an electron that has emitted an LO phonon is shown schematically. (c) Device currents as $V_{\mathrm{G}3}^{\mathrm{DC}}$ is swept (top) and $d{I}_c/d{V}_{\mathrm{G}3}^{\mathrm{DC}}$ on calibrated energy scale (bottom). (d) Colour map of $d{I}_c/d{V}_{\mathrm{G}3}^{\mathrm{DC}}$ taken at $B=12\mathrm{T}$ showing electron energy as a function of $V_{\mathrm{G}2}$ in regions where $n=1$, 2 electrons are pumped per cycle. (e) Potential profile through quantum dot during ejection of two electrons. (f) Data as in (d) but taken at $B=6\mathrm{T}$ where the emission of phonons gives side-peaks in the electron energy distribution.

Figure 2

(a) Barrier transparency $T$ (top left) and energy $E=-eV(t)$ (bottom left) as a function of time $t$ ($t_1$ is an arbitrary reference time centred at the electron arrival time). (Right) The shaded region represents the overlap of electron arrival-time distribution $\rho$ with barrier transparency $T$. (b) Experimentally measured $d{I}_c/d{V}_{\mathrm{G}3}^{\mathrm{DC}}$ on a colour scale as a function of $\Delta t_d$ and $V_{\mathrm{G}3}^{\mathrm{DC}}$ at $B=12\mathrm{T}$ and $A_d=-11\mathrm{dB}$. (c) Full width at half maximum $\delta V_{\mathrm{G}3}^{\mathrm{DC}}$ of the peaks in $d{I}_c/d{V}_{\mathrm{G}3}^{\mathrm{DC}}$ as a function of $\Delta t_d$ for different attenuation $A_d$ extracted by fitting to a Gaussian function. Double-peak structure is indicated with two arrows. (d) Numerical calculation results using the model described in the main text. (e) $\delta V_{\mathrm{G}3}^{\mathrm{DC}}$ calculated by the model.

Figure 3

(a) Experimentally observed $d{I}_c/d{V}_{\mathrm{G}3}^{\mathrm{DC}}$ on a colour map as a function of $V_{\mathrm{G}3}^{\mathrm{DC}}$ and $\Delta t_d$ when two electrons are pumped per cycle. The mid-point of the sinusoidal modulation, marked with arrows, was chosen as the point to deduce the shift in energy and time between the $E_1$ and $E_2$ features. Time delay between arrows is 350 ps. (b) Spectral map in the crossover regime ($\Delta t_d=2.5\mathrm{ns}$) showing the reversal of the order of the $E_1$ and $E_2$ lines. (c) Energy-Time domain sketch for the filtering of the arrival of the two electrons, whose probability density is represented by a diffuse circle using the parameters deduced from our simulation model described in the main text. When $d{V}_b(t)/dt$ is small between the arrival time of two electrons (i.e., the barrier is static or moving slowly) the lower-energy electrons are blocked as $V_{\mathrm{G}3}^{\mathrm{DC}}$ is swept (Case $i$). For a large $d{V}_b(t)/dt$ (rapidly moving barriers), faster than the threshold Case $ii$, the higher-energy electrons are blocked instead (Case $iii$). (d) Model of the observed current in (a): both of the two shaded areas have $I_c\simeq ef$ but the $E_2$ electron is transmitted on the left area and the $E_1$ on the right area.