In this work, we study the performance of the HP/Agilent/Keysight 3458A in the DCV mode. A Programmable Josephson Voltage standard (PJVS) system was used to generate step-wise approximated triangular waveforms which were sampled at 100 kHz with an aperture time of 1.4 mu s. We present the static gain error and non-linearity results at the highest sampling rate (100 kHz) for five 3458As. We find a consistent difference in behaviour for new Keysight-branded units compared to older units.

A method for traceability to SI for ac voltage and current based on high performance digitizers is presented. In contrast to the existing thermal-based methods, the proposed method utilizes direct traceability to quantum-based waveforms via the use of Josephson voltage systems. This allows not only a simplification of the traceability chain and reduced measurement times but also offers the potential for analysis of the ac voltage and current waveform spectral content, a feature which is not possible using thermal methods. Scaling of current and voltage is achieved by the use of current shunts and resistive voltage dividers respectively. Target operating ranges are up to 1 A and 100 V with a frequency range up to 1 kHz for both. The corresponding target uncertainty for this traceability route is 1 mu V V-1 and 2 mu A A(-1) up to frequencies of 1 kHz. The traceability chain is described and various components are characterized to validate their suitability for this task. It is demonstrated that these uncertainty targets can be met under certain conditions. The use of multi-tone calibration waveforms is investigated to further reduce measurement time. An uncertainty analysis method based on simulation using real component performance data is demonstrated.

We present the simulated performance of a Josephson traveling wave parametric amplifier based on a one-dimensional array of radio-frequency single-junction superconducting quantum interference devices. Using the capabilities allowed by the WRspice simulation platform and previous works on this scheme, we include in our study the effects of fabrication tolerances in the device parameters on the gain of the amplifier. Our simulations show the negative effects of parameter variation and the resulting microwave reflections of signal and pump waves between individual cells. We present a method to understand the inner dynamics of the device using an impedance model that substitutes the need to simultaneously consider phase bias points and wave mixing dynamics. This should allow the application of the results presented here to more complex schemes, which promise higher amplification and fewer drawbacks. We highlight the strict limitations on parameter spread in these devices while also discussing the robustness of the scheme to defects.

We have simulated the performance of the Josephson Travelling Wave Parametric Amplifier (JTWPA) based on the one-dimensional array of RF SQUIDs. Unlike the ideal model in which all SQUIDs are assumed to be identical, we allowed variation of the device parameters such as the geometric inductance of the SQUID loop, capacitance to ground, Josephson junction capacitance and critical current. Our simulations confirm the negative effects of variation of the device parameters leading to microwave reflections between individual cells and the shift of the flux bias from the optimal point. The strongest effect is caused by the variation of the geometric inductance as it varies both the wave impedance and the flux bias. The most detrimental, however, are point defects, such as shorts to ground making the circuit opaque to microwaves. This imposes stringent requirements on the fabrication process making it extremely challenging. We highlight the strict limitations on parameter spread in these devices while also discussing the robustness of the scheme to variation.

We present an analysis of wave-mixing in recently developed Josephson Travelling Wave Parametric Amplifiers (JTWPAs). Circuit simulations performed using WRspice show the full behaviour of the JTWPA allowing propagation of all tones. The Coupled Mode Equations (CMEs) containing only pump, signal, and idler propagation are shown to be insufficient to completely capture complex mixing behaviour in the JTWPA. Extension of the CMEs through additional state vectors in the analytic solutions allows closer agreement with WRspice. We consider an ordered framework for the systematic inclusion of extended eigenmodes and make a qualitative comparison with WRspice at each step. The agreement between the two methods validates both approaches and provides insight into the operation of the JTWPA. We show that care should be taken when using the CMEs and propose that WRspice should be used as a design tool for non-linear superconducting circuits such as the JTWPA.

The redefinition of the SI base units ampere and kilogram in 2019 formalized the use of the quantum Hall effect (QHE) to provide resistance traceability (the SI ohm) from the fundamental constants h and e. Traditionally, realization of the ohm via the QHE has required large complex liquid helium cryostats (including a high field superconducting magnet), and been largely confined to National Measurement Institutes. In recent years, graphene has been demonstrated as an ideal material for QHE samples, offering access to the quantum resistance reference (RK=h/e2) at lower magnetic fields and higher temperatures than previously possible. We present a system that builds on this technological advance, combined with liquid helium-free (closed cycle) cryogenic cooling techniques. The system integrates both a graphene QHE reference and a Cryogenic Current Comparator (CCC) instrument into a single compact enclosure. Resistance bridges based around a CCC offer the ultimate accuracy and noise performance for comparisons of conventional room temperature standard resistors to the QHE reference, and for scaling between different decade values, but this technology has not previously been demonstrated without the use of liquid helium. Our CCC system also integrates a second cryogenic SQUID detector to operate as the critical nanovoltmeter in the bridge electronics. We use a latest generation polymer-encapsulated molecular doped epigraphene sample optimized for operation at the 5 T field of our compact magnet, which does not require any user tuning of device properties on repeated cool-down cycles. Combined with the cryogen-free cooling, this gives a truly ‘turn-key’ system, making the quantum resistance reference and CCC accuracy available 24/7 in the metrology laboratory with no regular user intervention. The system is designed for both the realisation of the ohm at 100 Ω and regular calibration of standard resistors in the range 1 Ω to 10 kΩ, with combined relative standard uncertainties down to 0.01 ppm in the best cases.

We present measurements of microwave-induced Shapiro steps in a superconducting nanobridge weak link in the dissipative branch of a hysteretic current-voltage characteristic. We demonstrate that Shapiro steps can be used to infer a reduced critical current and associated effective local temperature. Our observation of Shapiro steps in the dissipative branch hows that a finite Josephson coupling exists in the dissipative state and thus can be used to put an upper limit on the effective temperature and on the size of the region that can be heated above the critical temperature. This work provides evidence that Josephson behaviour can still exist in thermally-hysteretic weak link devices and will allow extension of the temperature ranges that nanobridge based single flux quantum circuits, nanoSQUIDs and Josephson voltage standards can be used.

In this paper, a novel phase-locking technique is used to interface a Programmable Josephson Voltage Standard (PJVS) with a Keysight U8930B Performance Audio Analyzer. This technique uses both hardware and software to phase-lock the PJVS to the analyzer via a master clock. Both long term stability and nulling measurements were performed on the analyzer. The long term stability results indicated that the lowest Allan deviation was achieved after 500 s of sampling. The long term stability provides a springboard for the nulling measurements. The nulling measurements allows the possibility for the U8903B to be used as a reliable transfer of the ac quantum voltage standard.

Measurements of the resonant behavior of a cryogenic current comparator (CCC) under a range of damping conditions have been made. A model of conserved thermal-noise energy in resonant systems has been applied showing that, regardless of the value of the damping resistor, the energy stored in the resonance is constant. This finding is presented in the context of the design of high turn CCCs for use in the measurement of small currents where there is an increasing requirement to understand and reduce noise. Various damping methods for CCCs are described and experimental results compared with the theory.

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.

The pulse-driven Josephson Voltage Standard, also called Josephson Arbitrary Waveform Synthesizer (JAWS) is already well established for different applications in AC voltage metrology. To further increase the output voltage towards 10 V and to reduce the complexity of the JAWS systems we investigated two different approaches, which finally can be combined. One approach is to integrate an optimized on-chip power splitter to reduce the number of high-frequency (HF) channels from room temperature down to 4 K. A pulse pattern generator with less HF outputs will directly reduce the complexity and costs of a JAWS system. The second approach is to use an optical pulse-drive implementing cold photodiodes close to the JAWS chip. The use of optical fiber will have two main advantages: the optical fibers will reduce the high frequency noise and will enable an easy splitting into parallel optical channels. We will present first results with both approaches.

Precision measurement of DC and AC voltages requires an analogue to digital converter specification to have two key parameter values: the number of effective or noise free bits and the signal bandwidth. Commercial ADCs may offer the potential for use in a metrology class voltmeter but there is no easy way to compare the dynamic specification of a DMM with that of an ADC, especially when the number of bits or bandwidth changes. An architecture independent ADC/DMM figure of merit (FOM), is proposed to facilitate this comparison. At National Measurement Institutes, it is necessary to be able to measure with significantly greater precision than the device or instrument under test. Analysis shows that the FOM required of a metrology class ADC is beyond the state of the art for both ADCs and instruments. Fortunately, the use of superconducting Josephson junction based circuits offers the possibility to achieve the required precision. This paper gives the background to and reviews the progress of an EU funded research project for a quantum analogue to digital converter which is aiming to achieve the required FOM, beyond the state of the art.

This paper describes the design and simulation of a high order sigma-delta loop filter to use in a feedback loop for the QuADC project. The project target specifications required the selection of a fourth order feedback loop to achieve them. The design includes two loop rates (100 MHz and 20 MHz), and the selected loop was a cascade of integrators with feedforward topology. The simulation results show that the target specification can be achieved by configuring the oversampling ratio and the digital filter according to the measurement bandwidth.

An optoelectronic pulse drive system based on commercially available telecoms optoelectronic components and a field programmable gate array (FPGA) has been developed. The system was used to drive a Josephson junction array (JJA) to synthesize quantum-accurate voltage waveforms. Results from preliminary demonstration of the system are presented showing the synthesis of a 3.1 kHz sine wave.

A Programmable Josephson Voltage Standard (PJVS) has been used to calibrate a voltmeter by measuring the difference between a Digital to Analog Converter (DAC) and a step-wise approximated sine wave from a PJVS with a difference amplifier (DA). The characterization of two different DAs was used to determine the accuracy in transferring the PJVS value to the voltmeter, operating the DAC as a real-time calibrated transfer standard with an uncertainty of a few μV/V.

A compact design of a combined cryogenic current comparator and null detector assembly is described. The system is intended for integration in a four-terminal resistance ratio bridge to provide both current ratio and voltage ratio balance. The comparator and null detector are contained within the same superconducting shield having an overall diameter of less than 50 mm. The assembly is suitable for use in a wide-neck liquid helium cryostat or can be integrated in a cryogen-free apparatus.

We present a two-signal single flux quantum (SFQ) detection scheme for the purpose of reading out two pixels of a superconducting nanowire single photon detector (SNSPD). The circuit is based on a coincidence buffer element which is able to output a signal when both of its input lines are triggered. The circuit model for the SNSPD element is simulated in SPICE and optimized to match the experimental SNSPD response data. The two-signal detection scheme is simulated using JSIM which allows for the simulation of Josephson junction elements in a circuit. We demonstrate a model of the two-signal circuit operating with two simulated SNSPD pixel inputs and investigate the response of the scheme when a phase shift is applied to one of the inputs. The scheme shows potential as a useful coincidence detector of single photons. We also present preliminary experimental results of nanobridge-based Josephson junctions to be used in the realization of the coincidence detector circuit. Evidence of the nanobridges exhibiting Josephson behavior (SQUID modulation) are presented.