Towards single-electron metrology

We review the status of the understanding of single-electron transport (SET) devices with respect to their applicability in metrology. Their envisioned role as the basis of a high-precision electrical standard is outlined and is discussed in the context of other standards. The operation principles of single electron transistors, turnstiles and pumps are explained and the fundamental limits of these devices are discussed in detail. We describe the various physical mechanisms that influence the device uncertainty and review the analytical and numerical methods needed to calculate the intrinsic uncertainty and to optimise the fabrication and operation parameters. Recent experimental results are evaluated and compared with theoretical predictions. Although there are discrepancies between theory and experiments, the intrinsic uncertainty is already small enough to start preparing for the first SET-based metrological applications.Comment: 39 pages, 14 figures. Review paper to be published in International Journal of Modern Physics

Practical quantum realization of the ampere from the electron charge

One major change of the future revision of the International System of Units (SI) is a new definition of the ampere based on the elementary charge \emph{e}. Replacing the former definition based on Amp\`ere's force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from \emph{e}, accurate to within $10^{-8}$ in relative value and fulfilling traceability needs, is still missing despite many efforts have been spent for the development of single-electron tunneling devices. Starting again with Ohm's law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are quantized in terms of $ef_\mathrm{J}$ ($f_\mathrm{J}$ is the Josephson frequency) with a measurement uncertainty of $10^{-8}$. This new quantum current source, able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibrations of digital ammeters. Beyond, it opens the way to further developments in metrology and in fundamental physics, such as a quantum multimeter or new accurate comparisons to single electron pumps.Comment: 15 pages, 4 figure

Integrated quantized electronics: a semiconductor quantized voltage source

The Josephson effect in superconductors links a quantized output voltage Vout = f \cdot(h/2e) to the natural constants of the electron's charge e, Planck's constant h, and to an excitation frequency f with important applications in electrical quantum metrology. Also semiconductors are routinely applied in electrical quantum metrology making use of the quantum Hall effect. However, despite their broad range of further applications e.g. in integrated circuits, quantized voltage generation by a semiconductor device has never been obtained. Here we report a semiconductor quantized voltage source generating quantized voltages Vout = f\cdot(h/e). It is based on an integrated quantized circuit of a single electron pump operated at pumping frequency f and a quantum Hall device monolithically integrated in series. The output voltages of several \muV are expected to be scalable by orders of magnitude using present technology. The device might open a new route towards the closure of the quantum metrological triangle. Furthermore it represents a universal electrical quantum reference allowing to generate quantized values of the three most relevant electrical units of voltage, current, and resistance based on fundamental constants using a single device.Comment: 15 pages, 3 figure

Novel methods of fabrication and metrology of superconducting nanostructures

As metrology extends toward the nanoscale, a number of potential applications and new challenges arise. By combining photolithography with focused ion beam and/or electron beam methods, superconducting quantum interference devices (SQUIDs) with loop dimensions down to 200 nm and superconducting bridge dimensions of the order 80 nm have been produced. These SQUIDs have a range of potential applications. As an illustration, we describe a method for characterizing the effective area and the magnetic penetration depth of a structured superconducting thin film in the extreme limit, where the superconducting penetration depth $lambda$ is much greater than the film thickness and is comparable with the lateral dimensions of the device

Automated Setup to Accurately Calibrate Electrical DC Voltage Generators

At National Institute of Metrological Research (INRIM), an automated setup to calibrate DC Voltage generators, mainly top-level calibrators from 1 mV to 1 kV has been developed. The heart of the setup is an INRIM-built automated fixed ratios DC Voltage divider. The significant achievement of this setup is the possibility to interconnect the divider, a DMM characterized in linearity, a DC Voltage Standard and a DC Voltage generator under calibration and automatically to manage the calibration process. This calibration method allows to save a lot of time, to improve the reliability and to increase the accuracy of the calibration of generators. The relative uncertainties of the system span from 0.6x10-6 to 1.2x10-4 improving the previous capabilities of the INRIM laboratory for calibration of programmable multifunction instruments. In addition, this system allows to avoid the employment of several Standards (some of them still manually operating) carrying out the entire process without changing the setup configuration and without the presence of operators. The concept of this setup can be transferred to secondary high-level electrical calibration Laboratories that could be consider it useful for their calibration activities.Comment: 6 pages 8 figure

Coulomb blockade and Bloch oscillations in superconducting Ti nanowires

Quantum fluctuations in quasi-one-dimensional superconducting channels leading to spontaneous changes of the phase of the order parameter by $2\pi$, alternatively called quantum phase slips (QPS), manifest themselves as the finite resistance well below the critical temperature of thin superconducting nanowires and the suppression of persistent currents in tiny superconducting nanorings. Here we report the experimental evidence that in a current-biased superconducting nanowire the same QPS process is responsible for the insulating state -- the Coulomb blockade. When exposed to RF radiation, the internal Bloch oscillations can be synchronized with the external RF drive leading to formation of quantized current steps on the I-V characteristic. The effects originate from the fundamental quantum duality of a Josephson junction and a superconducting nanowire governed by QPS -- the QPS junction (QPSJ).Comment: 5 pages, 4 figure