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Josephson-based quantum voltage standards – an ongoing success story

Ralf Behr, Stephan Bauer, Marco Kraus, Oliver Kieler, L. Palafox

Published Jan 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.59161/wmbk4956

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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.
The advancement of quantum metrology is intrinsically linked to the development of nanoelectronic and quantum devices. The Programmable Josephson Voltage Standard (PJVS), a system comprising thousands of superconducting Josephson junctions with tunnel barriers on the nanoscale, provides a fundamental quantum-based AC voltage reference. However, extending this quantum traceability to harmonic power measurements, essential for modern power systems with extensive power electronics, remains a significant challenge. This work demonstrates a high-accuracy harmonic power standard by leveraging the unique quantum properties of a nano-fabricated PJVS array. We introduce a time-division calibration scheme where the precise voltage steps of the PJVS are used to calibrate a high-performance dual-channel analog-to-digital converter (ADC). This method bypasses the need for complex synchronous sampling and heavy computational algorithms, relying instead on the intrinsic accuracy of the Josephson quantum voltage. The system achieves a measurement uncertainty of 14 × 10 ×6 ( k = 2) for fundamental power and 50 × 10 −6 ( k = 2) for harmonic power up to the 60th order. Comparative tests with national primary standards show a maximum deviation of only 6 × 10 −6 for harmonic power metrology but also serves as a compelling demonstration of a practical, high-precision application for superconducting nanoelectronic devices, bridging the gap between quantum standards and industrial measurement needs.
We have recently created a 4 V rms cryocooled JAWS (Josephson Arbitrary Waveform Synthesizer) using 204,960 nearly identical Josephson junctions (JJs) that are embedded in coplanar-wave guides. The JJs are pulse-biased at repetition rates up to 16×109pulses per second to create quantum-accurate, calculable AC waveforms at frequencies from DC to greater than 1 MHz. This system has metrological applications including in precision ac voltage calibrations, comparisons of arbitrary impedances, and ac power measurements.
We review our development of Josephson-junction-based programmable reference sources to synthesize spectrally pure waveforms with quantum-based voltage accuracy for characterizing and improving future communication devices and systems. The goal is to provide sources that together span the entire radio frequency band, equivalent to seven orders of magnitude in frequency (20 kHz to 300 GHz). To synthesize waveforms in the microwave frequency band, we are extending the existing Josephson arbitrary waveform synthesizer (JAWS) technology used for ac voltage metrology at audio frequencies (<;20 kHz). Using new microwave circuits and experimental techniques, we demonstrate JAWS-based synthesis of single-tone waveforms at 1 GHz, with -49 dBm output power and 79 dBc spur-free dynamic range (SFDR). To synthesize waveforms in the millimeter-wave frequency band, we are exploiting single flux quantum (SFQ) superconducting digital technology to design circuits that amplify SFQ pulses using a network of pulse splitters. With our initial SFQ-based circuit, we demonstrate synthesis of a 4-GHz sine wave with -74 dBm output power and 70 dBc SFDR.
This paper presents the basic principle of the pulse-driven ac Josephson voltage standard, also called “Josephson arbitrary waveform synthesizer” (JAWS). We will mainly focus on activities and developments at the Physikalisch-Technische Bundesanstalt (PTB). The JAWS is suitable to generate high precision quantized waveforms, which can be arbitrarily programmed in the frequency and time domain with extremely high spectral purity (typical signal-to-noise ratios SNR of 120–140 dBc). A brief overview of the fabrication technology for highly integrated JAWS circuits with more than 50 000 junctions per chip will be described. This includes the stacked junction technology with up to 5-stacked junctions. The experimental setup and the key-features of JAWS will be shown too. New approaches designed to further increase the output voltage, to simplify the experimental setup, and to extend the range of applications are the on-chip power dividers, the optical pulse drive, and the RF-JAWS. A selected application of the JAWS is described to demonstrate the usability of sophisticated JAWS waveforms for the complex characterization of electrical devices. The PTB JAWS circuits already have a significant impact on the quantum ac voltage metrology community. JAWS chips made at PTB have been distributed to more than 10 national metrology and other research institutes within the framework of international research projects.
Recent metrological activities with programmable Josephson voltage standards (PJVS) are focused on extending the quantum accuracy to AC voltages, e.g. for the step-wise approximation of sine waves. Stimulated by the progress in this field, new requirements for the quality and availability of 1 V and 10 V circuits have been established. Based on the experience with programmable 1 V SINIS circuits fabricated at PTB and used at present by 13 National Metrological Institutes worldwide, the fabrication process and the microwave design were improved. The experience gained hereby enabled us to improve the properties of programmable 10 V SINIS arrays which were realized by us for the first time in 2000. The new 10 V circuits have 17 bit resolution and develop under 70 GHz microwave irradiation flat Shapiro steps at the 10 V level which are more than 600 muA wide. A direct comparison of the output voltage with a conventional 10 V SIS Josephson voltage standard confirmed the suitability for metrological applications. Incorporating 10 V-PJVS into existing AC metrology setups is expected to reduce their uncertainty budgets by about one order of magnitude.