Single Quantum Level Electron Turnstile

We report on the realization of a single-electron source, where current is transported through a single-level quantum dot ($Q$) tunnel coupled to two superconducting leads ($S$). When driven with an ac gate voltage, the experiment demonstrates electron turnstile operation. Compared to the more conventional superconductor–normal-metal–superconductor turnstile, our superconductor–quantum-dot–superconductor device presents a number of novel properties, including higher immunity to the unavoidable presence of nonequilibrium quasiparticles in superconducting leads. Moreover, we demonstrate its ability to deliver electrons with a very narrow energy distribution.

Figure 1

(a) Experimental current map of a superconductor–quantum-dot hybrid device as a function of gate and bias potential, in the absence of periodic gate drive (device $\mathcal{S}$). Colored solid lines correspond to the four superconducting gap edges as illustrated in (b). The device is operated as a single-level turnstile when its state is modulated periodically around its $(n,n+1)$ charge degeneracy point. The on-state currents are $I_{+}=290\mathrm{pA}$ (red) and $I_{-}=-250\mathrm{pA}$ (blue). (b) Energy diagram of the device with a small bias applied, illustrating electron tunneling events in and out the quantum dot. Grey areas indicate the amplitude range for solely forward tunneling, also seen in (a). Driving the turnstile with a square wave signal allows for tunneling to occur within a narrow energy window.

Figure 2

(a) Current-bias traces measured near the charge degeneracy point. Characteristic plateaus appear with $I=ef$ (indicated by dashed lines) when applying a small modulation signal (magenta, $A_{\epsilon }\approx 0.64\mathrm{\Delta }$, $f=190\mathrm{MHz}$; blue, $A_{\epsilon }\approx 1.0\mathrm{\Delta }$, $f=60\mathrm{MHz}$) to the gate. The black trace shows the current response with no ac gate drive. (b) Current-gate traces measured for $A_{\epsilon }\approx \mathrm{\Delta }$ and the same frequencies as in (a), at $V_B=\frac{3}{2}\mathrm{\Delta }/e$ (magenta) and $V_B=\mathrm{\Delta }/e$ (blue). (c) Current at the inflection point of the plateaus shown in (a) as a function of operation signal frequency. The insets highlight deviations of the normalized current $I/ef$ from 1 in both the low and high frequency ranges (all data are from device $\mathcal{S}$).

Figure 3

(a) Color map of $\partial I/\partial V_B$ as a function of bias and gate modulation amplitude ($f=56\mathrm{MHz}$, $\overline{\epsilon }={\overline{\epsilon }}_0$). Narrow blue regions corresponding to rapid increase in current separate areas of voltage-independent current (white), with values $I=0$ and $I=\pm ef$. (b) Color map of turnstile current as a function of static gate offset from degeneracy point and gate modulation amplitude ($f=60\mathrm{MHz}$, $V_B=1.5\mathrm{\Delta }/e$). All data are from device $\mathcal{A}$.

Figure 4

(a) Turnstile current as a function of operation signal amplitude (device $\mathcal{A}$, $f=56\mathrm{MHz}$, $\overline{\epsilon }={\overline{\epsilon }}_0$, and $e{V}_B=0.7\mathrm{\Delta }$). The sharp decrease in current indicates the sudden onset of backtunneling. The continuous line is the numerical calculation for the SQS with all parameters determined by the device dc transport properties (see text). The dashed line is the analogous calculation for a SINIS device with normal state resistance $R_N=300\mathrm{k}\mathrm{\Omega }$, $U=3.0\mathrm{\Delta }$ and assuming quasiequilibrium of electrons in $N$ by electron-phonon relaxation [38]. The arrows indicate the values of $A_{\epsilon }$ used in (c). (b) Slope at inflection point of $I(V_b)$ on the turnstile plateaus, averaged over $A_{\epsilon }$, as a function of temperature (device $\mathcal{A}$). The dashed line is the calculation for the SINIS device, with parameters as in (a). (c) Calculation of the energy distribution of the delivered charge per cycle, for different gate drive amplitudes $A_{\epsilon }$, with parameters as in (a). The negative part of the panel displays the backtunneling contribution. The highest position of the quantum dot level, as determined by the gate modulation, is represented in the inset by the lines of corresponding colors.