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PLoS ONE

A modular and customizable open-source package for quantum voltage standards operation and control

Paolo Durandetto, A. Sosso

Published Dec 17, 2018• 3 citations
Publisher

Abstract

This paper presents an open-source package developed in Python that controls and drives a programmable Josephson array to synthesize dc and ac quantum-accurate voltages. Programmable arrays are devices subdivided into independent subsections, each counting a number of series connected Josephson junctions that follows a binary sequence (1, 2, 4, 8, …) to control the output voltage. Our software allows to independently measure the current-voltage characteristics of each subsection by means of a set of arbitrary waveform generators and a nanovoltmeter that measures the voltage across the whole array with high sensitivity. A quantization test tool is also provided to check with sub-microvolt resolution whether the array is operating on its quantum margins. The code is modular and easily expandable with the support of many libraries, allowing prompt reconfiguration for different calibration and testing purposes. It is aimed at being a starting point for cooperation between National Metrology Institutes towards the realization of a shared quantum voltage calibration infrastructure.

DOI
10.1371/journal.pone.0209246

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This paper presents an open-source package developed in Python that controls and drives a programmable Josephson array to synthesize dc and ac quantum-accurate voltages. Programmable arrays are devices subdivided into independent subsections, each counting a number of series connected Josephson junctions that follows a binary sequence (1, 2, 4, 8, …) to control the output voltage. Our software allows to independently measure the current-voltage characteristics of each subsection by means of a set of arbitrary waveform generators and a nanovoltmeter that measures the voltage across the whole array with high sensitivity. A quantization test tool is also provided to check with sub-microvolt resolution whether the array is operating on its quantum margins. The code is modular and easily expandable with the support of many libraries, allowing prompt reconfiguration for different calibration and testing purposes. It is aimed at being a starting point for cooperation between National Metrology Institutes towards the realization of a shared quantum voltage calibration infrastructure.
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 design, fabrication, and the characterization of a 0.5-V Josephson junction array device are presented for the quantum voltage standards in the National Institute of Metrology (NIM) of China. The device consists of four junction arrays, each of which has 1200 3-stacked Nb/Nb x Si1−x /Nb junctions and an on-chip superconducting microwave circuit which is mainly a power divider enabling each Josephson array being loaded with an equal amount of microwave power. A direct current (dc) quantum voltage of about 0.5 V with a ∼1-mA current margin of the 1st quantum voltage step is obtained. To further prove the quality of NIM device, a comparison between the NIM device with the National Institute of Standards and Technology (NIST) programmable Josephson voltage standard (PJVS) system device is conducted. The difference of the reproduced 0.5-V quantum voltage between the two devices is about 0.55 nV, which indicates good agreement between the two devices. With the homemade device, we have realized a precise and applicable 0.5-V applicable-level quantum voltage.
Arrays of Josephson junctions have been used successfully for many years as the primary standard of voltage. A recent development has been the fabrication of arrays, based on non-hysteretic Josephson junctions, which allows the voltage output to be changed almost instantaneously. When these arrays are divided into binary segments a ‘digital-to-analogue converter’ with quantum accuracy is created. The properties of two types of array, a SINIS array, using intrinsic shunting of the Josephson junctions, and a SIS array with external, on-chip shunting have been investigated. The accuracy of the generated voltages and AC properties of the arrays when driven with a purpose-built, programmable current bias source are discussed. It is anticipated that a Josephson standard having waveforms with calculable rms values of AC voltage will soon be available.
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.
A pulse drive system capable of converting an arbitrary input signal into a delta sigma encoded pulse code stream in real time has been demonstrated. This system is based on the use of analog and digital hardware controlled by a Field Programmable Gate Array (FPGA) rather than using software to produce the delta sigma code and then loading it into the memory of a commercial Pulse Pattern Generator (PPG). The results of using the system to drive a Josephson junction array to synthesize quantum-accurate voltage waveforms are presented. The advantage of such a system includes the significant reduction in time required to change waveform parameters. This provides an easily tunable source of high-fidelity stable voltage waveforms at low temperature for future applications including validation of components for use in quantum technologies.