Single Cooper-pair pumping in the adiabatic limit and beyond

We demonstrate controlled pumping of Cooper pairs down to the level of a single pair per cycle, using an rf-driven Cooper-pair sluice. We also investigate the breakdown of the adiabatic dynamics in two different ways. By transferring many Cooper pairs at a time, we observe a crossover between pure Cooper-pair and mixed Cooper-pair-quasiparticle transport. By tuning the Josephson coupling that governs Cooper-pair tunneling, we characterize Landau-Zener transitions in our device. Our data are quantitatively accounted for by a simple model including decoherence effects.

Figure 1

The Cooper-pair sluice. (a) Equivalent circuit of the sluice and scheme of the measurement setup. (b) False-color scanning electron micrograph of a representative device. (c) Time evolution of the control parameters $J_1$, $J_2$, and $n_g$ for a typical pumping cycle.

Figure 2

Single Cooper-pair pumping. Pumped charge $Q_p$ vs peak-to-peak amplitude $\Delta n_g$ and offset $n_g^0$ of the gate drive. The data are taken at zero bias voltage $V_b$. The pumping frequency is $f=80\text{MHz}$. The flux pulses are tuned so that $J_{\min }=J_{\min }^0$ and $J_{\max }=0.8J_{\max }^0$. Dashed lines enclose the diamond-shaped regions where $Q_p/2e$ is expected to be constant and quantized (assuming ideal operation).

Figure 3

Crossover between pure Cooper-pair and mixed Cooper-pair-quasiparticle dynamics. (a) Pumped charge $Q_p$ vs gate offset $n_g^0$ for increasing gate amplitudes $\Delta n_g$ (bottom to top). Bias voltage and other pumping parameters are the same as in Fig. 2. (b) Circles: Same data as in (a), projected on the $n_g^0$ axis and plotted vs $\Delta n_g$. Dashed line: Asymptotic adiabatic-limit expectation. In both panels, the first three pumping plateaus are indicated by arrows.

Figure 4

Nonadiabatic pumping and Landau-Zener transitions. (a) Instantaneous energies of the ground (bottom set of curves) and first excited state (top set) vs time for a pumping period (the two sets of curves are obtained by modulating the parameter $J_{\max }$). In the model described in the text, nonadiabatic transitions are localized at level crossings, and occur with probability $P_{\text{LZ}}$. Decoherence induces complete dephasing between subsequent transitions, and relaxation via inelastic Cooper-pair tunneling (both are indicated by wavy arrows). (b) Normalized pumped charge $Q_p/Q_0$ vs Josephson coupling $J_{\max }$, for a set of frequencies in the range of 70 and 120 MHz. The gate pulse parameters are $n_g^0=0$ and $\Delta n_g=0.45$. The experimental traces (squares) are vertically offset by 0.2, and plotted together with the best fit of Eq. (1) to them (solid lines). (c), (d) Asymptotic pumped charge $Q_0$ vs $f$ (c) and $\lambda$ parameter vs $1/f$ (d) for three different measurement sets (squares, circles, and triangles). The solid line in (d) is a fit to the data of the expression $\lambda =f_0/f$.