Tunable Nonadiabatic Excitation in a Single-Electron Quantum Dot

We report the observation of nonadiabatic excitations of single electrons in a quantum dot. Using a tunable-barrier single-electron pump, we have developed a way of reading out the excitation spectrum and level population of the dot by using the pump current as a probe. When the potential well is deformed at subnanosecond time scales, electrons are excited to higher levels. In the presence of a perpendicular magnetic field, the excited states follow a Fock-Darwin spectrum. Our experiments provide a simple model system to study nonadiabatic processes of quantum particles.

Figure 1

(a) Schematic of the single-electron pump device and experimental circuit. (b),(c) The relation between the applied rf signal ($V_{\mathrm{rf}}$) and the electrostatic confinement potential at different parts of the cycle. (d),(e) Close-up of the confinement potential for step (ii) in (c) for cases of adiabatic (d) and nonadiabatic (e) changes in the potential. (f),(g) Pump current $I$ and $dI/d{V}_{G2}$ as a function of $V_{G2}$, taken with $B=6\mathrm{T}$ and $f=100\mathrm{MHz}$ (f) and 1 GHz (g). (h),(i) $dI/d{V}_{G2}$ as $V_{G1}$ and $V_{G2}$ are varied, taken with $f=100\mathrm{MHz}$ and 1 GHz, respectively, at $B=6\mathrm{T}$.

Figure 2

(a) Behavior of the pump current in perpendicular magnetic fields $B$ taken with $f=100\mathrm{MHz}$. $dI/d{V}_{G2}$ is plotted in a color scale. The regions of $Nef$ plateaux are marked by $N$. (b) $dI/d{V}_{G2}$ as in (a) but taken with $f=1\mathrm{GHz}$. A series of additional lines ($L1$, $L2$, and $L3$) appear in the plateau regions. (c) Data in (b) replotted to show the positions of the lines $L1$, $L2$, and $L3$ on the $V_{G2}$ axis relative to the $L0$ line. The dotted lines for $L1$, $L2$, and $L3$ show fits to Fock-Darwin states of a circular dot.

Figure 3

(a) Frequency dependence of the pump current at zero magnetic field. $dI/d{V}_{G2}$, rescaled to take into account the effect of a frequency change on the $ef$ value, is plotted in a color scale. (b) Frequency dependence at $B=6\mathrm{T}$, showing the excitation lines $L1$, $L2$, and $L3$ gradually appearing as $f$ increases. (c) Occupation probabilities of the ground state ($L0$) and excited states ($L1$, $L2$, and $L3$) deduced from the data in (b). The data for $L0$ are plotted against the left axis, while the rest are on the right axis.