Figure 1

(a) Colored micrograph of the Cooper pair pump consisting of a superconducting island shown as a red bar separated by a single Josephson junction and a SQUID. The energy levels of the island are controlled by the dc gate and the high-frequency pulse gate. The basic pumping principle and the corresponding pulse sequence are depicted in panels (b) and (c), where the solid line indicates the value of $V_{\mathrm{p}}$ in each phase. With this pulse sequence, Cooper pairs are transferred through the island against the bias voltage. Note that the positive pulse voltage shifts the electrostatic potential of the island down. (d) The combination of a resonant tunneling process (solid arrow) and an incoherent relaxation process (dashed arrow) leads to the positive current peaks observed in Fig. 2b.Reuse & Permissions

Figure 2

Current through the device as a function of the gate induced charge $\Delta Q_0/2e=V_{\mathrm{g}}{C}_{\mathrm{g}}/2e$ and the bias voltage $V_{\mathrm{b}}$ (a) without and (b) with the pumping sequence applied. At $\Delta Q_0/2e=0.32$, pumping of Cooper pairs is observed. For a direct comparison, cuts at ${\mathrm{eV}}_{\mathrm{b}}/E_{\mathrm{C}}=0.66$ from panels (a) and (b) are depicted in panel (c). (d) Pumped current as a function of the pulse length $\tau$ for forward (black squares) and backward (red dots) pumping. The coherent oscillations have a period of 160 ps and decay on a time scale of hundreds of picoseconds. Here, we employed $T_{\mathrm{r}}=8\mathrm{ns}$, ${\mathrm{eV}}_{\mathrm{b}}/E_{\mathrm{C}}=0.46$, and $n_{\mathrm{p}2}-n_{\mathrm{p}1}=2{\mathrm{eV}}_{\mathrm{b}}/8E_{\mathrm{C}}$. The insets show the continuously repeated pumping sequences in each case with the number of base sequences $n=1$. The continuous lines are simulations based on the Hamiltonian (1). (See text for details.)Reuse & Permissions

Figure 3

Pumping efficiency $\eta =I/I_{\max }$ as a function of the pumping period $T_{\mathrm{r}}$ for forward (black squares) and backward (red circles) pumping with the maximum efficiencies ${\eta }_{\max }=0.8$ and ${\eta }_{\max }=0.6$, respectively. The continuous lines are simulation including an energy relaxation rate of ${\Gamma }_1$ $=$ 8 ns. The maximum efficiency depicted in the inset for backward pumping shows behavior ${\eta }_{\max }\left(n\right)=A{\eta }_0^n$, where ${\eta }_0=0.74$ is the efficiency per pulse and $A$ is the efficiency independent of the number of pulses.Reuse & Permissions