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arXiv:0802.1364 · Physical Review Letters

Nonadiabatic Charge Pumping in a Hybrid Single-Electron Transistor

D. V. Averin, Jukka P Pekola

Published Aug 4, 2008• 82 citations
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Abstract

We study theoretically current quantization in the charge turnstile based on the superconductor-normal-metal single-electron transistor. The quantization accuracy is limited by either Andreev reflection or by Cooper-pair-electron cotunneling. The rates of these processes are calculated in the "above-the-threshold" regime when they compete directly with the lowest-order tunneling. By shaping the ac gate voltage drive it should be possible to achieve the metrological accuracy of 10;{-8}, while maintaining the quantized current on the level of 30 pA, just by one turnstile with realistic parameters using aluminum as a superconductor.

DOI
10.1103/physrevlett.101.066801

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We study theoretically current quantization in the charge turnstile based on the superconductor-normal-metal single-electron transistor. The quantization accuracy is limited by either Andreev reflection or by Cooper-pair-electron cotunneling. The rates of these processes are calculated in the "above-the-threshold" regime when they compete directly with the lowest-order tunneling. By shaping the ac gate voltage drive it should be possible to achieve the metrological accuracy of 10;{-8}, while maintaining the quantized current on the level of 30 pA, just by one turnstile with realistic parameters using aluminum as a superconductor.
First I discuss various candidates of single-electron current pumps for quantum metrology. Then I focus on the hybrid normal-metal-superconductor turnstile in the form of a one-island single-electron transistor with one gate. The device demonstrates robust current plateaus at multiple levels of ef at frequency f. I discuss the various error mechanisms, based on our experiments and theoretical considerations. Ultimately the quantization accuracy is expected to be limited by either two-electron tunneling or by Cooper-pair-electron co-tunneling. We predict that it should be possible to achieve the metrological accuracy of 10-8, while maintaining the quantized current on the level of more than 10 pA, just by one turnstile with realistic parameters using aluminium as a superconductor. Recently we have managed to run ten turnstiles in parallel increasing the current level to above 100 pA. Work on suppressing the harmful sub-gap leakage current is in progress with encouraging experimental results.
In a superconducting single-electron transistor (SSET), we demonstrate a charge turnstile regime based on higher-order tunneling as a major transport mechanism. In this regime, the quantized current appears as a sequence of Cooper pair-electron cotunneling events cycled by a periodic gate signal and transferring a discrete three-electron charge per cycle. Operating as a relatively slow, higher-order tunneling system, the 3e-turnstile exhibits stable current plateaus in the sub-pA range. The device could be useful for generating precise ultralow currents as well as for experimental evaluation of cotunneling error rates in electron turnstiles.
We consider the influence of the electromagnetic fluctuations on the transport properties of a hybrid single electron transistor, consisting of superconducting electrodes and a normal-metal island, when operated as a turnstile. We derive the analytic expressions for the rates near the thresholds of single electron tunneling, Andreev reflection, and Cooper-pair–electron cotunneling processes. These results show that the dissipative on-chip impedance suppresses the rates of the undesirable higher-order tunneling processes much stronger than the single electron tunneling which can therefore be utilized to increase the accuracy of such a device in quantum metrological applications.
We present an experimental study of hybrid turnstiles with high charging energies in comparison to the superconducting gap. The device is modeled with the sequential tunneling approximation. The backtunneling effect is shown to limit the amplitude of the gate drive and thereby the maximum pumped current of the turnstile. We compare results obtained with sine and square wave drive and show how a fast rise time can suppress errors due to leakage current. Quantized current plateaus up to 160 pA are demonstrated.
We present an experimental study of hybrid turnstiles with high charging energies in comparison to the superconducting gap. The device is modeled with the sequential tunneling approximation. The backtunneling effect is shown to limit the amplitude of the gate drive and thereby the maximum pumped current of the turnstile. We compare results obtained with sine and square wave drive and show how a fast rise time can suppress errors due to leakage current. Quantized current plateaus up to 160 pA are demonstrated.
Single-electron transistors have been proposed to be used as a read-out device for Cooper pair charge qubits. Here we show that a coupled superconducting transistor at a threshold voltage is much more effective in measuring the state of a qubit than a normal-metal transistor at the same voltage range. The effect of the superconducting gap is to almost completely block the current through the transistor when the qubit is in the logical state 1, compared to the mere diminishment of the current in the normal-metal case. The time evolution of the system is solved when the measuring device is driven out of equilibrium, the effect of higher-order contributions is examined and the setting is analyzed numerically for parameters accessible by lithographic aluminum structures.