Evidence of Cooper-pair pumping with combined flux and voltage control

We have experimentally demonstrated pumping of Cooper pairs in a single-island mesoscopic structure. The island was connected to leads through SQUID (superconducting quantum interference device) loops. Synchronized flux and voltage signals were applied whereby the Josephson energies of the SQUIDs and the gate charge were tuned adiabatically. From the current-voltage characteristics one can see that the pumped current increases in $1e$ steps which is due to quasiparticle poisoning on the measurement time scale, but we argue that the transport of charge is due to Cooper pairs.

Figure 1

(a) Scanning electron micrograph of the sample. The two input coils can be seen on the top and bottom, respectively. The gate extends to the far right and the gate capacitance is $C_{\mathrm{g}}=0.24\mathrm{fF}$ based on dc measurements. The current flows between the two leads on the left side. (b) Closeup of the island. The measured total capacitance of the island is 3.7 fF which corresponds to a charging energy of about 1 K for Cooper pairs. The maximum $E_{\mathrm{J}}$ per SQUID is estimated to be around 0.5 K based on the normal state resistance. (c) Schematic illustration of the measurement setup. We used commercial room temperature electronics for the current measurement and three synchronized arbitrary waveform generators for the control pulse. The external coil for tuning the background of the SQUIDs is at 20 mK. The voltage biasing happens via voltage division through resistive lines. A surface mount capacitor of 680 pF and an on-chip capacitor on the order of 10 pF (indicated by $C_{\mathrm{s}}$) were also used.

Figure 2

(a) Contour plot of the measured dc current at constant voltage against dc currents in the two input coils. The total variation in the current is around 40 pA at this bias point $\left(150\mu \mathrm{V}\right)$. The arrow line indicates the path along which the flux pulsing is performed in the pumping experiment. The lines of minimum current along which the arrows are aligned are the lines along which half a flux quantum threads one of the two SQUIDs. The slight tilting of the lines is a signature of the inductive cross-coupling. (b) Waveforms that were used in the experiment. The thin almost sinusoidal pulse is the gate signal for pumping in, say, the “forward” direction, and the dashed $\pi$-shifted signal is for pumping in the “backward” direction. The low level of the gate pulse is zero. The thick lines are the current signals corresponding to the arrowed path in the previous contour plot. The used gate signals were not perfectly sinusoidal but rather there was a dead time in the three signals such that the minima of the $E_{\mathrm{J}}$’s and the extrema of the gate charge would coincide with better certainty. The shallow dips in the current signals compensate for the inductive cross coupling. (c) Contour plot of the measured current at a constant voltage of $250\mu \mathrm{V}$ against the relative phase differences between the signals with the pumping signal being applied at 2 MHz. The blue circle is the optimal choice for pumping “forward” while the red circle is the optimal point for pumping “backward.” The amplitude was set large (over $400e$) and the variation in current was 150 pA. This operation point is far from optimal, but we still obtain a clear modulation for calibration purposes. The color scales in (a) and (c) are relative and in units of pA.

Figure 3

(a) Examples of measured $I\text{−}V$ curves with the pumping signal applied at 3 MHz. The gate charge (in $2e$ units) varies between 4 and 34. The solid curves correspond to pumping forward and the dashed curves correspond to pumping backward. Here $V_{\mathrm{meas}}$ is the measured value of voltage over the pump. (b) Difference of current, $\mathrm{\Delta }I$, in the $I\text{−}V$ curves of (a) for pumping in opposite directions. The dotted lines indicate the expected values.

Figure 4

(a) Difference $\mathrm{\Delta }I$ in current of forward and backward pumping at 2.5 MHz against the high level of the gate signal $V_{\mathrm{g}}^{\mathrm{hi}}$ with the low level at zero. The dashed lines are drawn at $2ef$ intervals. (b) Large gate amplitude behavior of $\mathrm{\Delta }I$ at a few frequencies. The dashed lines show the expected gate dependence, i.e., their slope is $2ef$. The curves are offset for clarity. (c) Fitted slopes to the data of the previous plots up to $V_{\mathrm{g}}{C}_{\mathrm{g}}∕e=10$ are shown by circles. The solid line indicates the expected behavior. The voltage bias point was around $10\mu V$ in all the above plots.