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Conference on Precision Electromagnetic Measurements

Exploiting First and Second Shapiro Steps Towards the Reduction of Bias Lines in Programmable Josephson Arrays

Paolo Durandetto, A. Sosso

Published Jul 1, 2018• 3 citations
Publisher

Abstract

Quantum Digital-to-Analog Converters (DACs) based on programmable Josephson array (PJVS) represent the most advanced devices currently employed in ac voltage calibrations. Pulse-driven Josephson technology, compared to PJVS, provides cleaner and faster voltage signals and is the main topic of frontier developments. Although the extension of PJVS frequency range appears to be arduous, some enhancement are still practicable. In this work we demonstrate the possibility of synthesizing stepwise quantum voltage waveforms with half of the bias lines and fewer Josephson junctions by exploiting both first and second Shapiro steps, with no losses in terms of performances.

DOI
10.1109/cpem.2018.8500828

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Quantum Digital-to-Analog Converters (DACs) based on programmable Josephson array (PJVS) represent the most advanced devices currently employed in ac voltage calibrations. Pulse-driven Josephson technology, compared to PJVS, provides cleaner and faster voltage signals and is the main topic of frontier developments. Although the extension of PJVS frequency range appears to be arduous, some enhancement are still practicable. In this work we demonstrate the possibility of synthesizing stepwise quantum voltage waveforms with half of the bias lines and fewer Josephson junctions by exploiting both first and second Shapiro steps, with no losses in terms of performances.
Quantum digital-to-analog converters (DACs) based on programmable Josephson array [Programmable Josephson Voltage Standard (PJVS)] represent the most widely used quantum standard in ac voltage calibrations. The extension of PJVS frequency above the kilohertz range appears to be arduous; however, some enhancements are still practicable. In this work, we demonstrate the possibility to advantageously operate a conventional binary-divided PJVS array with a reduced number of bias lines. This feature is achieved by exploiting both the first and the second Shapiro steps along with nonconventional DAC codings. Two newly devised bias techniques are described in detail and preliminary experimental tests on waveform synthesis have been carried out and are presented here.
An alternating programmable Josephson voltage standard (AC-PJVS) configured as a multibit digital-to-analog converter has been developed to explore the staircase-approximated waveforms synthesis at frequencies up to the acoustic range. The AC-PJVS setup is based on state-of-the-art modular electronics able to bias individually the subsections of a binary-divided array consisting of 8192 intrinsically shunted SNIS junctions. High order Shapiro steps have been employed for waveform synthesis having amplitude beyond 1 V by finely trimming the SNIS temperature using a two stage cryocooler. Alongside the experiments on the synthesis, the experimental setup was improved for direct comparisons between quantum staircase waves and conventional sine waves based on the use of a room temperature-operating phase sensitive detector and on a differential precision sampling system. Both methods maximize the accuracy obtained from the AC-PJVS synthesizer, allowing, in principle, its use for primary LF AC voltage metrology.
We propose a new method for transient-error-free AC voltage waveform synthesis using a programmable Josephson voltage standard (PJVS) array. Stepwise-approximated sinusoidal waveforms generated using PJVS can be potential tools for AC voltage calibration or related applications. However, the transient error caused by the transitions between quantized voltage steps is a crucial problem for some applications. By driving a PJVS array using high-speed periodical pulse packets and conventional DC biases, the influence of the transitions can essentially be eliminated. This paper describes the basic idea of our new method for driving a PJVS array.
This paper presents recent advances in the application of binary-divided 1 V array, consisting of 8192 intrinsically shunted SNIS overdamped Josephson junctions (JJs), for the synthesis of stepwise waves with quantum accuracy. The maximum output voltage is ensured by opportunely driving the subsections of the SNIS array by means of three states bias-current setpoints to the Shapiro steps n = 0, ±1 or n = ±2, respectively. Reconfigurable digital modular electronics has been designed to bias individually each of the 13 subsections of the SNIS array. A two-stage closed cycle refrigerator equipped with LF and RF electrical lines is employed for cooling-down the SNIS array for temperatures ranging from 3.6 K to above 7 K. Stepwise sine waves with rms amplitude ranging from 1 to 2 V using the first (n = 1) and second (n = 2) Shapiro steps, different temperatures and bias-current setpoints have been synthesized up to the kHz range. The synthesized waves have been recorded and analyzed by a high-precision differential sampling system. We report the results of the first characterizations carried out with the new multibit current source and an improved version of the sample holder designed to optimize the heat dissipation of the SNIS array for operation in cryocooler setups.
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 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.