Nathan E. Flowers-Jacobs

Performance Improvements for the NIST 1 V Josephson Arbitrary Waveform Synthesizer

The performance of the NIST Josephson arbitrary waveform synthesizer has been improved such that it generates a root-mean-square (rms) output voltage of 1 V with an operating current range greater than 2 mA. Our previous 1 V JAWS circuit achieved this same maximum voltage over a current range of 0.4 mA by operating every Josephson junction in its second quantum state. The newest circuit synthesizes 1 V waveforms with the junctions operating in the first quantum state. The voltage per array is doubled because the number of junctions in each array was doubled through the use of improved microwave circuit designs that increased the bias uniformity to the junctions. We describe the circuit improvements and device operation, and we demonstrate the system capabilities by showing measured spectra of a 1 Hz sine wave and a dual-tone waveform. With only two arrays of the new circuit, we also synthesized a 128 mV sine wave without a compensation bias signal, which is one of the bias signals required for achieving 1 V. This is the same rms output voltage achieved with the previous circuit using four arrays.

Two-Volt Josephson Arbitrary Waveform Synthesizer Using Wilkinson Dividers

The root-mean-square (rms) output voltage of the National Institute of Standards and Technology (NIST) Josephson arbitrary waveform synthesizer (JAWS) has been doubled from 1 V to a record 2 V by combining two new 1 V chips on a cryocooler. This higher voltage will improve calibrations of ac thermal voltage converters and precision voltage measurements that require state-of-the-art quantum accuracy, stability, and signal-to-noise ratio. We achieved this increase in output voltage by using four on-chip Wilkinson dividers and eight inner/outer dc blocks, which enable biasing of eight Josephson junction (JJ) arrays with high-speed inputs from only four high-speed pulse generator channels. This approach halves the number of pulse generator channels required in future JAWS systems. We also implemented on-chip superconducting interconnects between JJ arrays, which reduces systematic errors and enables a new modular chip package. Finally, we demonstrate a new technique for measuring and visualizing the operating current range that reduces the measurement time by almost two orders of magnitude and reveals the relationship between distortion in the output spectrum and output pulse sequence errors.

A Boltzmann Constant Determination Based on Johnson Noise Thermometry

A value for the Boltzmann constant was measured electronically using an improved version of the Johnson Noise Thermometry (JNT) system at the National Institute of Standards and Technology (NIST), USA. This system is different from prior ones, including those from the 2011 determination at NIST and both 2015 and 2017 determinations at the National Institute of Metrology (NIM), China. As in all three previous determinations, the main contribution to the combined uncertainty is the statistical uncertainty in the noise measurement, which is mitigated by accumulating and integrating many weeks of cross-correlated measured data. The second major uncertainty contribution also still results from variations in the frequency response of the ratio of the measured spectral noise of the two noise sources, the sense resistor at the triple-point of water and the superconducting quantum voltage noise source. In this paper, we briefly describe the major differences between our JNT system and previous systems, in particular the input circuit and approach we used to match the frequency responses of the two noise sources. After analyzing and integrating 49 days of accumulated data, we determined a value: k = 1.380 642 9(69)×10-23 J/K with a relative standard uncertainty of 5.0×10-6 and relative offset -4.05×10-6 from the CODATA 2014 recommended value.

Josephson-based full digital bridge for high-accuracy impedance comparisons*

This paper describes a Josephson-based full digital impedance bridge capable of comparing any two impedances, regardless of type (R-C, R-L, or L-C), over a large frequency range (from 1 kHz to 20 kHz). At the heart of the bridge are two Josephson arbitrary waveform synthesizer systems that offer unprecedented flexibility in high-precision impedance calibration, that is, it can compare impedances with arbitrary ratios and phase angles. Thus this single bridge can fully cover the entire complex plane. In the near future, this type of instrument will considerably simplify the realization and maintenance of the various impedance scales in many National Metrology Institutes around the world.

Josephson-based full digital bridge for high-accuracy impedance comparisons

This paper describes a Josephson-based impedance bridge capable of comparing any types of impedance over a large bandwidth. The heart of the bridge is a dual AC Josephson Voltage Standard (ACJVS) source which offers unprecedented flexibility in high-precision impedance calibration (i.e., calibration at arbitrary ratios and phase angles) allowing full coverage of the complex plane using a single bridge.

2 Volt pulse-driven josephson arbitrary waveform synthesizer

We describe a new generation of Josephson Arbitrary Waveform Synthesizers that generate programmable ac waveforms with an rms amplitude of 3 V and, at 1 kHz, have a quantum locking range greater than 1 rnA. This system has two chips with a total of 204 960 Josephson junctions (JJs) co-located on a cryocooler. To test for systematic errors, we phase-shift by 180° the waveform generated by half the JJs (102 480 JJs) to produce an approximate null. The measured residual of 51 nV rms implies a relative agreement of 3 parts in

Josephson Arbitrary Waveform Synthesizer with Two Layers of Wilkinson Dividers and an FIR Filter

10^{8}

Direct comparison of a pulse-driven Josephson arbitrary waveform synthesizer and a programmable Josephson voltage standard at 1 volt

between the two halves of the system.

The NIST Johnson Noise Thermometry System for the Determination of the Boltzmann Constant

The output voltage of Josephson arbitrary waveform synthesizers (JAWS) is limited by the number of Josephson junctions (JJs) that can be driven by a single pulse-generator channel. Here, we double the number of JJs driven by one generator channel to 51 200 JJs by distributing the pulse bias between four JJ arrays by use of two layers of Wilkinson dividers. We use this single bias to generate a voltage at 1 kHz with an rms magnitude of 1 V. This voltage is quantum-accurate over an operating current range of 1.4 mA. For comparison, the operating current range of a recent design that uses a single layer of Wilkinson dividers is twice as large, but requires two pulse-bias channels to generate 1 V. We also show that we can recover this performance by incorporating in the pulse generator a finite-impulse response (FIR) filter that acts as an equalizer. The FIR filter creates a custom transfer function that compensates for the bandwidth-limited transfer function of the Wilkinson dividers. Optimizing the FIR filter parameters increases the operating current range from 1.4 to 2.7 mA. This ability to drive additional JJ arrays with a single pulse-generator channel will enable future JAWS chips and systems to achieve significantly larger output voltages. This will increase the voltage range for JAWS calibrations of ac thermal converters and improve precision voltage measurements that require quantum-accurate, stable, and distortion-free waveforms with a large signal-to-noise ratio.

Impact of the latest generation of Josephson voltage standards in ac and dc electric metrology

We have performed direct ac comparisons between two types of quantum voltage standards, a pulse-driven Josephson arbitrary waveform synthesizer and a programmable Josephson voltage standard, at 1 V rms amplitude and a frequency of 100 Hz. The system architectures for these two Josephson technologies are quite different. However, in the range where their capabilities overlap, they should produce identical results. This comparison under various test conditions is a powerful method for verifying ideal performance of the systems, and exploring a number of potential systematic errors in both measurement methods and system operations.