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IEEE Transactions on Instrumentation and Measurement

Maximizing the Resolution of a Dual RF Drive Programmable Josephson Voltage Standard

D. Georgakopoulos

Published Mar 4, 2015• 4 citations
Publisher

Abstract

A dual radio frequency drive programmable Josephson voltage standard can generate quasi-continuous voltages with quantum accuracy. This paper focuses on the mathematical methods used to maximize the achievable voltage resolution and describes two algorithms that can be employed. Quasi-continuous voltages with a resolution of a few nanovolts have been achieved using Josephson junction arrays with missing junctions and an almost arbitrary segment structure.

DOI
10.1109/tim.2015.2406054

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Conference on Precision Electromagnetic Measurements•Jul 8, 2024•0 citations
A dual radio frequency drive programmable Josephson voltage standard can generate quasi-continuous voltages with quantum accuracy. This paper focuses on the mathematical methods used to maximize the achievable voltage resolution and describes two algorithms that can be employed. Quasi-continuous voltages with a resolution of a few nanovolts have been achieved using Josephson junction arrays with missing junctions and an almost arbitrary segment structure.
We have developed a programmable Josephson voltage standard that can produce voltages up to 20 V with a resolution of better than 0.1 µV over the whole voltage range and better than 1 nV for voltages up to 10 mV. The standard has two superconductor–normal metal–superconductor junction arrays connected in series and driven by two radiofrequency oscillators. The cryogenic part of the standard is based on a cryocooler. The new standard agrees with the primary quantum voltage standard maintained at the National Measurement Institute, Australia, within 10 nV and forms the basis of an automated calibration system for digital multimeters and voltage references.
Abstract Josephson voltage standards (JVSs) provide a primary realization of the volt, the unit of electromotive force. They generate direct current (dc) voltages up to 10 V and show agreement better than 1 nV V−1 at 10 V. For JVSs based on Josephson junction arrays (JJAs) that are driven by sinusoidal radiofrequency (RF) power, commonly referred to as continuous wave-driven JJAs (CWD JJAs), the minimum voltage that can be generated is limited to the voltage across one Josephson junction (JJ) for practical devices. To achieve this resolution, they may require a perfect JJA chip. JVSs based on a pulse-driven (PD) JJA require high performance electronics (i.e. high bandwidth, low distortion and jitter, pulse shaping filters and large memory) to achieve their minimum and maximum voltage. We have combined two CWD JJAs and two PD JJAs driven by two microwave inputs to one chip to generate quasi-continuous dc voltages up to the sum of the full-scale voltages of both JJAs that are robust to the imperfections of the JJs and have relaxed requirements on the RF electronics driving the JJA, compared to the existing CWD JVSs and PD JVSs, respectively. By use of the JJA chip at the National Measurement Institute Australia, we demonstrate its feasibility to generate voltages up to 1 V. Preliminary evaluation of the system shows that the voltage uncertainty can be 11 nV (k = 2) or better and the theoretical resolution is better than 1 nV from 0 V to 1 V. The main requirement is that all the JJs must have quantum locking ranges with respect to the power and frequency of the RF bias and for the PD JJAs to have a constant voltage over a range of dc bias current. Although this development is not a replacement for existing state-of-the-art JVSs, we anticipate that it will be an alternative fit-for-purpose solution for metrological applications under non-ideal operating conditions or when the components of the state-of-the-art solutions are not available.
The past few decades have witnessed great progress being made from the first voltage standards based on arrays of Josephson junctions. Continuous improvements in the fabrication process have increased the quality and “user-friendliness” of these superconducting circuits. Combined with the improvements in measuring electronics, the range of applications of Josephson-based measurements with unmatched precision has extended from DC into AC voltage metrology for signal frequencies up to 500 kHz. In this poster we will present several Josephson-based measurement systems developed for metrology applications. Two versions of quantum AC standards will be used as Josephson references: Programmable Josephson Voltage Standards (PJVS), which are based on serial arrays with up to 300,000 Josephson junctions, and pulse-driven arrays with more than 50,000 junctions, typically referred to as Josephson Arbitrary Waveform Synthesizers (JAWS). PJVS can reach amplitudes of up to 80 V, while pulse-driven arrays can reach up to 1 V or even 4 V. The advantage of pulse-driven Josephson voltage standards is that they are ideally suited as quantum-based voltage synthesizers for arbitrary waveforms or sine waves with high spectral purity. Therefore, they can be used directly to characterize or calibrate ADCs. In addition, JAWS are particularly useful in Josephson impedance bridges, which perform automated impedance calibrations at the 10-9 uncertainty level over a wide frequency range from 50 Hz to 80 kHz in a single bridge. We will further show how PJVS are used in commercial quantum voltmeters for DC and AC voltages and are typically used as quantum voltage references in measurement systems. Using differential sampling based on PJVS, uncertainties at the level of a few parts in 108 for frequencies up to the kHz range can be achieved. Such quantum-based AC voltage calibrations are at least 30 times faster than conventional AC-DC transfer and offer even better uncertainties. This idea has been quickly adopted by many National Metrology Institutes to establish such systems for AC voltage calibrations. As an example, the BIPM will now start worldwide onsite comparisons to ensure the uniformity of the new method which we introduced in 2006. But developments continue. Recently, a sub-sampling technique was used to extend the frequency range of the AC quantum voltmeter to up to 100 kHz with uncertainties below 5 parts in 106. In addition, a novel method, also for differential sampling, enables the measurement of arbitrary waveforms and the calibration of specific tones. Our poster will provide an overview of these Josephson-based metrological applications and present the latest developments from this fast-developing area.
The DC voltage across a Josephson junction is exactly determined by the number of single flux quanta Φ0passing the junction per second. By locking this flux train to an external sinusoidal microwave with the frequency f or a pulse train with the pulse rate f in such a way that one flux quantum is transferred per microwave period or per pulse respectively, the junction DC voltage becomes V=Φ0f in the simplest case. The precision of V is only determined by the uncertainty of the frequency control. As the output voltage is relatively small (V=140μV for f=70GHz), large series arrays of n Josephson junctions must be used to increase the voltage to practical levels V=nΦ0f. With a sinusoidal 70 GHz microwave drive and series arrays of up to 14000 SIS tunnel junctions modern DC voltage standards were developed in the past which may reach a reproducibility of a few parts in 10-10. These standards are commercially available and form the basis of the legal voltage metrology of most of the national laboratories worldwide. Because the reference voltages of these standards are widely overlapping it is difficult to rapidly adjust the desired voltage. It was therefore impossible to use these quantum voltmeters for the precise analysis of AC voltages. For this purpose the arrays had to be modified in many respects. The direct way to generate arbitrary Josephson waveforms V(t) is to rapidly alter the frequency f(t) with respect to the desired waveform V(t)=nf(t)Φ0. It requires a precise flux transfer control over a very wide frequency range.
Pulse-driven Josephson junction arrays (PD JJAs) are used for the generation of arbitrary waveforms with quantum accuracy. The main requirement for quantum operation is that all the Josephson junctions have quantum locking ranges (QLRs) with respect to the power and frequency of the radio frequency (RF) bias and constant voltage over a range of dc bias currents. In this paper we investigate the QLR of PD JJAs for the generation of dc voltage. Our results demonstrate that in proximity to the QLR for RF power, the dc current-voltage characteristics can show apparent quantization of the voltage with statistical properties almost indistinguishable from those in the QLR.