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Proceedings of the IEEE

Application of the Josephson effect to voltage metrology

Samuel P. Benz, C.A. Hamilton

Published Sep 20, 2004• 101 citations
Publisher

Abstract

The unique ability of a Josephson junction to control the flow of magnetic flux quanta leads to a perfect relationship between frequency and voltage. Over the last 30 years, metrology laboratories have used this effect to greatly improve the accuracy of dc voltage standards. More recent research is focused on combining the ideas of digital signal processing with quantum voltage pulses to achieve similar gains in ac voltage metrology. The integrated circuits that implement these ideas are the only complex superconducting electronic devices that have found wide commercial application.

DOI
10.1109/jproc.2004.833671

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The unique ability of a Josephson junction to control the flow of magnetic flux quanta leads to a perfect relationship between frequency and voltage. Over the last 30 years, metrology laboratories have used this effect to greatly improve the accuracy of dc voltage standards. More recent research is focused on combining the ideas of digital signal processing with quantum voltage pulses to achieve similar gains in ac voltage metrology. The integrated circuits that implement these ideas are the only complex superconducting electronic devices that have found wide commercial application.
The performance of programmable voltage signals that exploit the quantum behavior of superconducting Josephson junctions continues to improve and enhance measurements in metrology, communications, and quantum control. We review advances in pulse-driven digital synthesis techniques with Josephson-junction-based devices. Quantum-based synthesis of voltage waveforms has been demonstrated at frequencies up to 3 GHz and rms amplitudes up to 4 V. Josephson pulse generators have also been used to control and characterize superconducting qubits.
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 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.
Applications to electronics are mainly based on Josephson junctions special properties. As it was pointed before, a single Josephson junction is a perfect voltage to frequency converter (AC Josephson effect). One example is the application into RF amplifiers where a radiofrequency signal generates a magnetic flux in a circuit coupled to, for example, DC-SQUID. Josephson effect allows converting the flux into the SQUID to an amplified voltage signal, proportional to the number of 0. That is the base of the microwave applications. The SQUID inductance together with the capacitance of the junction, allows also using the device as resonator.
As thorough readers of this book have begun to discover by this chapter on metrology, the most widely used applications of superconducting electronics involve measurements of electromagnetic phenomena. Unlike most other phenomena used for measurements, superconductivity is also essential for electrical standards. Because it is a quantum phenomenon, it can represent voltage in terms of fundamental constants with an amazing precision of a few parts in 1019. In some regards superconducting voltage standards based on arrays of Josephson junctions are the most successful application of superconductivity, considering the numbers of junctions and their worldwide use. While they are conceptually simple, it has taken almost 50 years for their underlying technology to progress from unreliable single junctions to robust, complex, three-dimensional integrated circuits having more than 300,000 junctions and producing precision ac voltages up to 10 V. Here is their story.
Recently we designed and successfully tested a prototype of a superconducting digital-to-analog converter (DAC) based on processing single flux quantum (SFQ) pulses. Two unique features make the device very attractive for metrology applications: (i) The generation of output voltage is based on the fundamentally accurate Josephson frequency-to-voltage relationship. (ii) The device does not require any external signals with frequencies higher than 100 MHz. It is expected that the DAC will be used as a key component of novel standards and calibrators of ac voltage with frequency up to 1 MHz. The implemented prototype has low magnitude of output voltage (about 10 mV) which is far lower than the 1 to 10 V target magnitude.