2

In this talk, I will report primarily NIST results and progress in quantum-based voltage metrology. I want 

to thank all of the current and former staff, guest researchers and collaborators at NIST, as well as those 

colleagues and researchers at other national measurement institutes for the work that they've done in the 

field that provides the foundation for our current research.
3

When I tell people that I do metrology and standards at NIST, they usually shake their heads in 

understanding and say, “Oh, so you study the weather and storms?”

No, that is meteorology. In metrology, we study measurement.
4

In particularly, at NIST and other metrology laboratories around the world, we pursue better 

measurement and develop new technology and techniques for making better measurements. The staff in 

my Superconductive Electronics Group at NIST develop voltage standards based on the quantum effects 

of a device called a Josephson junction. We also exploit the zero resistance state of superconducting 

wires to reduce measurement uncertainty from voltages produced by currents on resistive leads.
5

What is a standard? It is a device or system that yields a repeatable value when appropriately measured. 

A quantum standard, such as voltage and resistance standards, exploits quantum effects that enable 

measurements to be intrinsically accurate so that repeatable values can be achieved in any laboratory 

using comparable systems, and in fact in any location in the universe. Such quantum- based electrical 

standards are different from all non-quantum standards for this very reason, and their success has lead the 

international community to redefine the international system of units and how we assign uncertainty 

through measurements of fundamental constants. The reproducibility of quantum standards for voltage 

and resistance through the Josephson and quantum Hall effects are the impetus for these changes. 

However, there is one caveat, they must be “appropriately” measured using best practices to reveal their 

accurate values and I will emphasize this important point throughout the talk.

Here are four background references:

J. Niemeyer, Handbook of Appl. Supercond., Vol 2: Applications (IOP, Bristol, 1998), p. 1813.

C. A. Hamilton, Rev. Sci. Instrum., vol. 71, p. 3611 (2000).

R. L. Kautz, Rep. Progr. Phys., vol. 59, p. 935 (1996).

B. Jeanneret and S. P. Benz, “Application of the Josephson effect in electrical metrology,” Proceedings of 

the International School on “Quantum Metrology and Fundamental Constants,” Les Houches, France, 1-12 

October 2007, eds. F. Piquemal and B. Jeckelmann, published jointly by EDP Sciences and Springer Verlag in The 

European Physical Journal Special Topics, vol. 172, pp. 181-206, June 1, 2009.
6

For over 40 years, research laboratories worldwide have worked to develop Josephson voltage standard 

technology for various applications. In this talk, I'm not going to review all the progress and measurement 

records because there are numerous review papers with all the references. Their have been four main 

instruments that have been developed at NIST and this map shows the locations of all the NISTdeveloped systems and chips. Prior to 1995, the conventional Josephson voltage standard was the 

quantum standard for realizing dc voltages. In this talk, I will focus primarily on the three newest systems 

that have been developed in order to achieve new capabilities, like ac voltage synthesis. These include the 

programmable JVS (PJVS), the Josephson arbitrary waveform synthesizer (JAWS), and the quantum 

voltage noise source (QVNS). These systems are each at different levels of development, and

performance.

As a result of decades of development, NIST versions of these 4 devices and instruments now reside on 6 

continents.
7

Applications of these JVS systems are primarily for calibration measurements of electrical instruments. 

PJVS systems are used for directly calibrating Zener voltage references. Some calibration labs, for 

example, will calibrate racks of Zener reference standards and return them to other labs and locations. 

PJVS systems are also used to measure the gain and linearity of electrical instruments like digital 

voltmeters and to calibrate electric power standards for low frequency AC. In addition to calibration, 

PJVS systems are used in a number of precision metrology experiments, such as measuring the kilogram, 

which is currently the artifact standard for mass. It is also a measurement of Planck’s constant. There is a 

plan to redefine the international system of units, the SI, in the coming years, after which the kilogram 

mass standard will be replaced with a mechanical and electrical comparison measurement.

So the PJVS are typically at 10 V output level and used for D.C measurements. The 2 V JAWS system is 

newer and its output voltage used to be only at a quarter voltage. But this technology has dramatically 

advanced in the last two years, increasing the output by a factor of ten. It's used as an intrinsic ac standard 

for calibrating meters and other standards. More recently, two 1 V JAWS systems have been used to 

realize a quantum-based impedance measurement. I’ll show one slide of this work.

Finally, there is a very low voltage instrument containing 6 Josephson junctions used as a voltage 

waveform synthesizer to calibrate low-noise electronics to make a primary thermometer based on 

measuring the Johnson noise of a resistor. This same quantum voltage noise source (QVNS) is also being 

used as a precision measurement of Boltzmann’s constant. This measurement is very similar to the 

Planck/ constant/kilogram experiment in that it is a thermal and electrical comparison.
8

At the conclusion of this talk, I hope you will have a greater appreciation for the following important 

point. What are the features of a quantum standard what makes it different from all the other instruments 

in your labs?

These metrology applications include dc and ac voltage, impedance, primary thermometry, and hopefully 

in the future radio-frequency communications.

In order to achieve a quantum-accurate voltage measurement, at a minimum, one needs a quantum-based 

circuit/device, an understanding of the error sources, and a well-characterized measurement technique 

that minimizes and accounts for those errors.

However, for a person who is neither an expert in superconductivity nor cryogenics to achieve a quantum 

accurate voltage measurement, they need a practically useful standard instrument that is sufficiently 

automated, enough to remove those errors. This requires careful circuit design exploiting both 

superconducting properties and the Josephson effects of Josephson junctions, devices made using a 

superconductive circuit fabrication process that reproducibly yields nearly identical junctions, cryogenic 

design and packaging of the devices and cryostats that optimizes thermal management of the circuits and 

systems, and well-engineered software that enables automation of the system, measurements and error

analysis.
9

So what are the features of a quantum voltage standard? The intrinsic accuracy must be derived from a 

quantum behavior. You might already be familiar with the atomic clocks and the quantum Hall effect. 

The electrical properties of the Josephson effect is the quantum behavior that produces the intrinsic 

accuracy of voltage standards. A quantum voltage standard always produces an accurate voltage 

regardless of environmental conditions or location, and thus identical voltages can be reproduced 

anywhere in the world or in the universe for that matter. This is in contrast to artifacts standards like the 

kilogram mass, as well as voltage standards based on electrochemical batteries. Such artifact standards 

were accurate for their time because they were manufactured to be nearly identical and environmentally 

stable, but their values still depended on manufacturing variations and changed with environmental 

conditions (temperature, humidity, pressure, etc), and over periods of time (aging). In contrast, a quantum 

standard generates reproducible and identical values for a range of bias parameters and operating 

conditions, and its value is insensitive to the environment and aging. Such values that remain constant as 

a function of varying bias conditions are called “flat spots”, and I'll show you some of these for our PJVS 

and JAWS systems. In order to ensure quantum accuracy, flat spots must be measured repeatedly and 

regularly to ensure that the devices are in their quantum states before, during and after measurements. So 

imagine an unchanging value of voltage that results every time you use the standard, or move it between 

different labs even on different continents.

Nevertheless, there are limitations to the accuracy of quantum standards. For example, thermal voltages 

generated by resistive leads traversing the cryogenic environment from 4 K to room temperature always 

affect the measurement of dc voltages. AC voltage errors affecting the JAWS system can arise from 

frequency-dependent error currents produced by impedance parasitics within the superconducting circuit, 

or impedances and losses of the measurement leads and the load of the instrument being calibrated. 

Minimizing systematic errors through optimized design of the instrument and measurement technique is 

critical and all remaining errors must be understood and characterized.
10

The values produced by artifact standards depend on environmental conditions, although they can be 

very stable, they will still change with time. Quantum based standards are intrinsically precise and 

accurate. More than 3 order of magnitude improvement in uncertainty with Josephson arrays.

The artifact standard for voltage that was in use for many decades of the last century is a chemical battery 

called a Weston cell. The technology to duplicate these standards was very good such that their agreement 

over short periods of time was typically 50 parts in a million provided they were maintained under 

controlled environmental conditions.

When the Josephson effect was discovered in 1962, metrologists began trying to realize voltage standards 

made with a few Josephson junctions. There were able to produce small accurate millivolt voltages that 

immediately improved the agreement between laboratories by two orders of magnitude. Over the next 

two decades, researchers around the world worked to increase the output voltage of the conventional 

Josephson voltage standard to achieve practical voltages of 1 V and then 10 V, which led to another 100-

fold improvement in agreement.

This required many years of gradually improving fabrication technology for the junctions, microwave 

designs to bias them, and understanding the physics of chaotic effects. More recently, comparisons of 

programmable Josephson voltage standards have improved agreement by another 10-fold, primarily 

because the PJVS produces stable quantized voltage steps that can be measured for longer periods of time 

thus reducing measurement noise. Thus, metrologists are continually looking for ways to replace artifacts 

standards with quantum standards for many different applications. Quantum voltage standards, in 

particular, have improved our ability to measure voltage by over 5 orders of magnitude, which has led to 

advances in measurements and also the performance of electrical instruments.

C. A. Hamilton, Rev. Sci. Instrum., vol. 71, p. 3611 (2000).

S. P. Benz, “Synthesizing Accurate Voltages with Superconducting Quantum-Based Standards,” IEEE

Instr. Meas. Magazine, p. 8 (2010).

A. Rüfenacht et al., "10 volt automated direct comparison of two cryocooled programmable Josephson 

voltage standards," 30th Conference on Precision Electromagnetic Measurements (CPEM 2016) Digest, 

presented 10–15 July 2016, Ottawa, Canada, pp. 25. DOI: 10.1109/CPEM.2016.7540474.
11

A Josephson junction is a weak link between two superconductors, and the weak link is typically either 

an insulator or a normal non-superconducting metal.

Paired electrons in each superconducting electrode can be described by a many- particle wavefunction 

that has both an amplitude and phase. This phase can maintain its coherence over macroscopic distances 

because the superconductor is a macroscopic condensate analogous to the now familiar Bose-Einstein 

condensate.

Josephson predicted two remarkable effects of such a junction:

(1) a supercurrent will flow through the weak link even at zero voltage difference, where  is the 

phase difference between the electrode wave functions, and the critical Ic is the maximum supercurrent 

that the junction can support.

(2) if a voltage difference is applied across the junction, then the phase difference evolves in 

proportion to the voltage, where the proportionality constant is the ratio of Planck’s constant to twice the 

electron charge, h/2e. These equations show that the junction’s supercurrent oscillates at a frequency 

exactly proportional to the voltage.
12

Thus a Josephson junction behaves similar to a harmonic oscillator in that the supercurrent oscillates at a 

frequency precisely proportional to its voltage. More importantly, the phase difference evolves by 

precisely 2 for each oscillation period and the junction voltage generates exactly one voltage pulse. 

Equally importantly, the time-integrated area of every pulse is precisely h/2e. Thus, phase periodicity of a 

junction leads to pulse quantization and voltage accuracy.
13

A junction biased with a dc remains in the zero-voltage quantum state until the bias exceeds its critical 

current. This positive and negative current range of this state defines the “flat spot”.

Biased above Ic, the junction continuously pulses and the supercurrent oscillates at a frequency 

proportional to the voltage. If a microwave signal or a periodic pulse bias is applied, then the oscillations 

lock and entrain to the frequency of that alternating bias, just like a driven harmonic oscillator. The 

supercurrent oscillations lock to the drive creating constant voltage flat spots over a range of dc bias. The 

oscillations also lock at harmonic multiples of the drive frequency, where the junctions generate multiple 

pulses for each period of the drive. The current range of each flat spot depends on the electrical properties 

of the junction and the applied ac bias.
14

Unfortunately, h/2e is small, about 2 μV/GHz, so that the voltage steps are spaced at about 40 μV for a 

typical periodic drive of 20 GHz. At least 1 V or 10 V are required for practical calibration of electronic 

instruments and other voltage standards. Thus, many junctions must be series connected to produce 

useful voltages. Fortunately, the quantized voltages of each junction will be identical when biased with 

the same frequency. The challenge, however, is that the current ranges of each step should also be similar 

so the larger combined voltage of the series- array of junctions can be selected with a common dc bias. 

This requires excellent junction uniformity and microwave power distribution. Many years of voltage 

standard development were required to find optimal materials for the junction barriers to achieve the 

junction uniformity, to improve the fabrication process of those junctions, and to achieve uniform power 

distribution of the ac biases. In addition to nearly identical current ranges of many quantum states, 

voltage accuracy also requires that the frequency of the ac bias source be referenced to an atomic clock

frequency.
15

The programmable Josephson voltage standard was invented in order to create an ac voltage source with 

quantum-based accuracy. It’s designed ability to rapidly select different quantized voltage steps enabled 

the step-wise approximated sign waves to be synthesized. The drawback of this approach was that, 

although the voltage steps were accurate, the transitions between them were not. Thus, it is not an 

intrinsic ac voltage source. Differential sampling, which compares these step voltages with other ac 

signals, has proven to be the best measurement approach for ac signals with frequencies less than 200 Hz 

and voltages greater than 1 V. This approach is primarily used for calibrating ac power meters.

The Josephson arbitrary waveform synthesizer, on the other hand, is an intrinsic ac voltage standard. It 

accomplishes this by controlling every quantized pulse in a digitally synthesized waveform, so every 

junction is always in one of three quantum states, generating either positive or negative pulses, or none. 

JAWS produces intrinsically accurate sine waves that have proven useful for ac voltage metrology at 

frequencies below 20 kHz. In addition to sine waves, the JAWS direct digital synthesis with quantized 

voltage pulses allows intrinsically accurate arbitrary waveforms that can be used for other applications. 

The quantum voltage noise source is essentially a low-voltage version of JAWS with only six junctions 

that generates pseudo-noise waveforms having a comb of harmonic tones of equal amplitude spread over 

bandwidths of a few megahertz.
16

Here are the features of the three modern voltage standard systems. The PJVS is microwave biased, 

produces programmable dc voltages up to 10 V and is used for dc voltage calibrations and ac voltage and 

power calibrations at frequencies below 200 Hz. The JAWS and QVNS systems are both pulse driven 

circuits that use digital sampling techniques to synthesize dc and ac signals. Recently, a maximum output 

voltage of 2 V rms was achieved for JAWS. It is an intrinsic ac standard. The QVNS produces arbitrary 

waveforms with peak amplitude up to 2 μV. A pseudo- noise waveform of harmonic combs of tones of 

identical amplitude are used as a calibration source for Johnson noise thermometry.

I’ll now describe each of these systems in more detail.
17

Next, I describe the basic operation, features and applications of the programmable Josephson voltage 

standard.
18

The Programmable Josephson voltage standard was invented in 1995 by Clark Hamilton. The PJVS 

circuit consists of a long series array of many junctions that is divided into smaller sub-arrays. The output 

voltage is programmed by individually biasing each array to one of the three quantized voltages. The 

number of junctions in the smallest arrays typically follow a ternary sequence to optimize voltage 

resolution with respect to the number of bias leads.

These low-speed bias currents typically switch at a few microseconds.

C.A. Hamilton, C.J. Burroughs, and R.L. Kautz,, “Josephson D/A converter with fundamental accuracy,” 

IEEE Trans. Instrum. Meas., vol. 44,

no. 2, pp. 223-225, Apr. 1995.

S. P. Benz, et al., “Stable 1-Volt programmable voltage standard,” Appl. Physics Lett., vol. 71, pp. 1866-

1868, Sep. 1997.

[8] C. J. Burroughs, et al., “1 Volt dc programmable Josephson voltage standard,”

IEEE Trans. Appl. Supercon., vol. 9, pp. 4145-4149, Jun. 1999.
19

NIST superconducting integrated circuits are fabricated in the Boulder Microfabrication Facility. The 10 

V PJVS chips contain over 265,000 junctions on a (12 mm x 17 mm) chip. The junctions consist of 

niobium superconducting electrodes and conductive barriers made of amorphous niobium-doped silicon. 

The microwave signal with a typical 20 GHz is supplied to 32 parallel arrays of junctions through a 4-

stage power divider circuit consisting of lumped element superconducting inductors, capacitors, power 

splitters and coplanar waveguides.

Many years of research and development, including simulation and modeling, were needed to optimize 

the materials, fab process, circuit elements and microwave designs.

A. Rüfenacht, L. Howe, A. E. Fox, R. E. Schwall, P. D. Dresselhaus, C. J. Burroughs, and S. P. Benz, 

“Cryocooled 10 V Programmable Josephson Voltage Standard,” IEEE Trans. Inst. Meas., vol. 64, no. 6, 

pp. 1477-1482, 2015.
20

These current-voltage characteristics of 16 identical arrays, having 16,800 junctions each, show that all 

the junctions in the array can be commonly biased on the same quantized voltage step. Furthermore, the 

excellent uniformity of both the junctions and the applied microwave biases results in overlapping flat 

spots covering a 2 mA current range.

A. E. Fox et al., “Junction Yield Analysis for 10 V Programmable Josephson Voltage Standard Devices,” 

IEEE Trans. Appl. Supercond., vol. 25, no. 3, pp. 1101505-5, 2015.
21

New cryopackage features and challenges that were solved include: heat sinking of the chip to a copper 

header, LHe or cryocooler interchangeability, fast interconnection with socket connections for low-speed 

biases and output voltage that enables swappable packages, a flexible interconnect matrix that enables 

reconfigurable sub-arrays to optimize array flat spots by allowing different sub- arrays to be grouped 

together.

The chip is soldered to the copper block and connected to the pcb via wirebonds. The package is 

compatible with both 1 inch diameter liquid helium cryoprobes and mounting on a cryocooler cold plate. 

For the dip probe configuration, a flexible pcb wraps the low speed bias leads to the back of the block, 

where a solder- configurable matrix enables connections be made between the chip and the connector. 

This eliminates the need to directly solder to the pcb and encodes the configuration information right on 

the package.

Optimized thermal management of the cryopackage enhances the resulting system performance by 

managing heat dissipated on the chip for different bias configurations.

L. Howe, A. E. Fox, A. Rüfenacht, C. J. Burroughs, P. D. Dresselhaus, S. P. Benz, and R. E. Schwall, 

“NIST 10 V Programmable Josephson Voltage Standard System Using a Low-Capacity Cryocooler,” 

IEEE Trans. Appl. Supercond., vol. 25, no. 3, pp. 1400404-4, June 2015.
22

This is the fully integrated NIST PJVS system, including the cryocooler, microwave synthesizer, 

voltmeter and temp controller, the DACs and an amplifier for DC biases, and a computer.

Operation of the chip in a cryostat allows the system to be fully automated, because a human operator is 

not required to raise or lower the chip into a liquid helium dewar. It also allows temperature to become a 

performance optimizing variable so that flat spots can be further optimized as a function of temperature.

Optimization and routine checking of flat spots is fully automated with software. Separate application 

software is used for different calibration functions, which allows metrologists and engineers to use the 

system without expertise in either cryogenics or Josephson devices.

NIST has made available identical versions of its PJVS system as a Standard Reference Instrument.
23

I’d like to say a few things about accuracy and stability. Use of a quantum standard does not ensure 

accuracy. In addition to known systematic errors, output voltages can be very stable and reproducible, 

even when circuits are biased off the edge of a flat spot, such as when one or a few junctions are not in 

their quantum states. Such stable, yet inaccurate values can yield measurements with very low uncertainty 

that give the appearance of accuracy. Thus, the publication of small uncertainties reported for a 

measurement is not the evidence of accuracy.

It is, therefore, very important to check that the circuits are always operating in quantum states by varying 

the biases and changing grounding configurations that might redistribute error currents.

Once again, system automation is an important tool for evaluating the quantum states of the system.

Appropriate measurement techniques are also necessary to measure and account for systematic errors, 

such as removing thermal voltages by reversing the PJVS dc voltage to opposite polarities, or by use of 

differential sampling to avoid non- quantized voltages from ac measurements.

A. Rüfenacht, et al., “Precision differential sampling measurements of low- frequency voltages 

synthesized with an ac programmable Josephson voltage standard,” IEEE Trans. Inst. Meas., vol. 58, pp. 

809-815, April 2009.

J. Lee et al., "An ac quantum voltmeter based on a 10V programmable Josephson array", Metrologia. vol. 

50, p. 612, (2013).
24

A video showing the how the voltage varies with respect to these two bias parameters is available at: 

Quantum State Flat Spots https://www.nist.gov/pml/quantum-electromagnetics/superconductiveelectronics/quantum-state-flat-spots

This slide shows the PJVS 10 V flat spot as a function of both microwave amplitude and common dc bias 

offset. You can see that the quantization vanishes at the lowest microwave bias shown, and reaches a 

maximum of about 1.8 mA dc range for applied power greater than -2 dBm. Similar flat spot 

measurements are typically taken as a function of cryocooler temperature, as well as at different 

microwave frequencies, to determine the best operating conditions for each device.

A. Rüfenacht, L. Howe, A. E. Fox, R. E. Schwall, P. D. Dresselhaus, C. J. Burroughs, and S. P. Benz, 

“Cryocooled 10 V Programmable Josephson Voltage Standard,” IEEE Trans. Inst. Meas., vol. 64, no. 6, 

pp. 1477-1482, June 2015.
25

This slide reiterates the main applications of the PJVS for calibration and precision measurements. The 

best comparison between two programmable Josephson voltage standards has shown agreement with an 

uncertainty of 3 parts in 10^11. For ac measurements of calibration instruments, the measurement 

uncertainty is less than 1 part in 10^6 for frequencies below 500 Hz.
26

Now we will move on to intrinsic ac voltage standards and arbitrary waveform synthesis.
27

Synthesis of ac voltages with intrinsic accuracy is possible using the same type of junctions as are used 

for the PJVS, but biased with pulses instead of microwaves, thereby precisely controlling all quantized 

voltage pulses at every point in time. The Josephson arbitrary waveform synthesizer is essentially an 

oversampled three-state digital to analog converter that is clocked at 15 GHz. The three states are pulses 

of both polarity and zero and they enable bipolar voltage waveforms to be synthesized. JAWS circuits 

typically synthesize dc and sine wave voltages which are used to calibrate thermal voltage converters and 

other ac voltage standards. They have primarily been implemented at frequencies below 20 kHz, where 

frequency- dependent systematic errors are typically less than a part in 10^6. In the past few years, JAWS 

circuits have achieved record rms amplitudes of 1 V.

J. Przybysz, A. Worsham , S. P. Benz, and C. A. Hamilton, Josephson Junction Digital to Analog 

Converter for Accurate AC Waveform Synthesis, Pat. No. 5,812,078, Sept. 22, 1998.

S. P. Benz and C. A. Hamilton, A pulse-driven programmable Josephson voltage standard, Applied 

Physics Letters, Vol. 68, pp. 3171- 3173 (1996).

S. P. Benz, C J. Burroughs, C. A. Hamilton, and T. E. Harvey, AC and DC Bipolar Voltage Source Using 

Quantized Pulses, Pat. No. 6,236,344, May 22, 2001.
28

The measurement paradigm for ac voltage is based on rms detectors called thermal voltage converters 

that thermally compare ac voltages with dc voltages. The ac-dc difference response of these artifact 

standard detectors depends on frequency and amplitude. Their response is very reproducible and stable 

with respect to environmental conditions, and they achieve their lowest measurement uncertainties below 

a part in 10^6 at 1 V. RMS detection also offers the feature of low sensitivity to signals at other 

frequencies, such as emi.

In comparison, JAWS systems are intrinsically accurate ac voltage sources, not detectors. They have 

demonstrated three orders of magnitude improvement in measurement uncertainty over thermal 

converters for small signals below a few millivolts. With the recent achievement of the first 1 V JAWS 

systems, the first direct comparisons with 1 V calibrators has just recently become possible.
29

Voltage calibrators are also ac sources and they typically produce voltages with uncertainties of a few 

parts in 10^5. A recent comparison of 1 V signals synthesized by two JAWS systems agreed to within a 

measurement uncertainty of a part in 10^7. We expect this agreement to dramatically improve in the 

coming years.

However, important and unwanted systematic errors are present in JAWS systems, and they can reach 

parts in 10^6 at a few kilohertz and the errors increase with increasing frequency. Research and 

development of JAWS circuits and JAWS bias techniques have the potential to further optimize the 

systems and reduce these systematic errors so they can be used at higher frequencies, eventually up to a 

few megahertz.

N. E. Flowers-Jacobs, A. Rüfenacht, A. E. Fox, P. D. Dresselhaus, and S. P. Benz, "2 volt pulse-driven 

Josephson arbitrary waveform synthesizer," 30th Conference on Precision Electromagnetic Measurements 

(CPEM 2016) Digest, presented 10–15 July 2016, Ottawa, Canada, p. 152.
30

The second one-voltage JAWS chip contained 51,240 total junctions distributed equally into four arrays. 

Each pair of adjacent arrays was biased with a common high-speed pulse sequence that was divided with 

a broadband power splitter and ac coupled to each array through on-chip dc blocks. Similar to the PJVS 

circuit, the arrays are connected in series through inductive low-pass filters. When generating a 1 V sine 

wave by clocking the bias pulses at 15 GHz, the JAWS circuit controls 770 trillion quantum states 

per second. Thus many quantum states must be quickly controlled to produce quantum-accurate ac 

voltages with flat spots.

The following examples showing spectra and flat spots were measured with a 24- bit delta-sigma analogto-digital converter with very low noise and very low intrinsic nonlinearity that produces minimal 

harmonic distortion.

N. E. Flowers-Jacobs, A. E. Fox, P. D. Dresselhaus, R. E. Schwall, and S. P. Benz, "Two-volt Josephson 

arbitrary waveform synthesizer using Wilkinson dividers," IEEE Trans. Appl. Supercond., vol. 26, no. 6, 

pp. 1400207-7, Feb. 2016.
31

This is a spectrum of the first quantum-accurate synthesized waveform of 2 V rms amplitude. The 

spectrum remains unchanged, showing no harmonic distortion from the JAWS signal over a 1 mA current 

range (flat spot). The very small (more than 123 dB below the fundamental) and visible harmonic 

distortion is from measurement ADC, and there are measurement techniques other than the flat spot bias 

changes that are used to confirm this.

With this record high output voltage, this is the best spectrum with the lowest distortion that we have ever 

measured with a JAWS signal, probably because the ADC performs better at this higher voltage.

N. E. Flowers-Jacobs, A. E. Fox, P. D. Dresselhaus, R. E. Schwall, and S. P. Benz, "Two-volt Josephson 

arbitrary waveform synthesizer using Wilkinson dividers," IEEE Trans. Appl. Supercond., vol. 26, no. 6, 

pp. 1400207-7, Feb. 2016.
32

A video showing the how these measured data vary with respect to these two bias parameters (pulse 

amplitude and current bias offset) is available at: 

Quantum State Flat Spots https://www.nist.gov/pml/quantum-electromagnetics/superconductiveelectronics/quantum-state-flat-spots

In this slide, we show the flat spots of all the quantum states of the 2 V dual-chip circuit as a function of 

the waveform period. In one plot we show how flat spot in voltage changes with a common current bias 

offset through all of the junction. The color shading indicates deviation from quantum accuracy as the 

difference in the voltage from the 2 V sine wave.

The spectrum in the upper right figure plots the data as measured over a ±0.55 mA range of current bias 

offset and its inset shows the nominal rms voltage. The spectrum shows the same minimal harmonic 

distortion of the digitzer as that shown in the previous slide.

The lower right figure, shows the flat spot as a function of the pulse amplitude of the total harmonic 

distortion (THD), measured also over the 1.1mA total offset range.

When the pulse amplitude is tuned to either edge of the THD flat spot, then the quantum-state shrinks 

with a bias offset that becomes smaller than the 1.1 mA range. This causes the voltage to deviate from the 

quantized value and an increase in harmonic distortion (and THD) that scales with the voltage deviation.

N. E. Flowers-Jacobs, A. E. Fox, P. D. Dresselhaus, R. E. Schwall, and S. P. Benz, "Two-volt Josephson 

arbitrary waveform synthesizer using Wilkinson dividers," IEEE Trans. Appl. Supercond., vol. 26, no. 6, 

pp. 1400207-7, Feb. 2016.
33

The JAWS applications are summarized here for ac voltage calibration of standards, converters and 

calibrators. The programmability and intrinsic accuracy of JAWS systems is also useful characterizing the 

gain and linearity of many other electronic instruments, like ADCs and amplifiers. Very recently, the two 

1 V JAWS systems enabled the first application of quantum ac voltage metrology to impedance 

calibrations. The arbitrary waveform capability of JAWS has been exploited for over a decade to 

characterize the analog electronics used to measure Boltzmann’s constant. I will briefly describe these 

two applications in the remaining slides.
Traditional bridge measurement methods for electrical impedance rely on calibrated transformer ratios 

and inductive voltage dividers. Such methods require many unique hardware configurations, one for each 

impedance ratio and impedance type (typically 1:1, 10:1, or quadrature ratios). A METAS (Swiss Federal 

Institute for Metrology) and NIST collaboration demonstrated a new quantum-based system using a full 

digital bridge and two 1 V JAWS systems. The JAWS programmability and accuracy, for the first time, 

enable impedance ratio measurements over the full complex impedance plane at any ratio and without 

needing any hardware modifications. This bridge also allows impedance ratio measurements to be 

performed over a larger frequency range (50 Hz to 50 kHz) because the JAWS systems have perfect 

linearity, high resolution, and the ability to adjust their relative phases. The system also eliminates the 

need for component calibration because it doesn’t require calibrated transformers or inductive dividers 

such as those required for conventional impedance bridges. It will greatly simplify dissemination of the 

impedance scale because it can directly compare any complex impedance (R, L, or C) to the dc quantum 

Hall resistance value (12.906 k), or to any other complex impedance.

F. Overney et al., "Josephson-based full digital bridge for high-accuracy impedance comparisons,” 

Metrologia, vol. 53, p. 1045, June 2016.
35

Finally, I’ll briefly describe the quantum voltage noise source (QVNS) that is being developed as a 

primary temperature standard and is currently being used for an electronic measurement of Boltzmann’s 

constant.
36

The Kelvin, one of the seven base SI units, is defined by an artifact standard, namely the triple point of 

water, whose temperature is set to 273.16 K. In addition, there are fixed-point artifact standards for 14 

defined temperatures covering the International Temperature Scale of 1990 (ITS-90) from 0.65 K to 

1,357.77 K. In 2000, additional points were added that extend the scale to millikelvin temperatures. The 

scale is designed to “represent” thermodynamic temperature and temperatures between the fixed points 

must be interpolated. A reproducible, scalable, primary thermodynamic standard is needed and an 

electronic one is being developed that is based upon quantum voltage synthesis and Johnson noise 

thermometry (JNT).

NIST first developed its QVNS-JNT system to investigate deviations of the International Temperature 

Scale of 1990 (ITS-90) from thermodynamic temperature at temperatures in the range of 505 K – 933 K, 

which overlaps the ranges of both acoustic gas-based and radiation-based thermometry. The success of 

these measurements led to its use as an “Electronic Kelvin” that links the SI kelvin to quantum-based 

electrical measurements, which produced an electronic determination of Boltzmann’s constant.

The international metrology community plans to fix the value of the Boltzmann constant, which would 

then redefine the Kelvin as part of a larger effort to link all units to fundamental constants. This approach 

would be the most stable and universal way to define measurement units, essentially eliminating all 

remaining artifact standards, such as those based on physical objects or substances like triple points.

D. R. White and J. Fischer, “The Boltzmann constant and the new kelvin,” Metrologia, Vol. 52, No. 5, 

pp. S213–S216 (Aug. 2015). doi:10.1088/0026-1394/52/5/S213
37

A number of researcher teams are developing JNT precision measurement systems and voltage 

synthesizers whose waveforms are based on the quantized voltage pulses generated by Josephson arrays. 

The QVNS developed at NIST is one of these synthesizers. This intrinsically accurate voltage calibration 

source is the heart of an electronic-based JNT, which determines temperature from the Johnson-Nyquist 

noise of a resistor. Typically, a 100 Ω resistor at the triple point of water is used to produce an extremely 

small ~1.2 nV/Hz1⁄2 noise voltage. Since this voltage is comparable to the noise of typical low-noise 

amplifiers, cross-correlation electronics must be used to measure the small voltage noise signals, and is 

typically measured over a 600 kHz bandwidth and integrated for many days in order to reduce the 

statistical measurement uncertainty below a part in 10^5. The QVNS synthesizes accurate, reproducible 

multitone waveforms that are intentionally designed to be comparable to the white noise of the resistor 

noise source. These pseudo-noise waveforms are constructed by summing many sine waves of different 

harmonic frequencies that have identical amplitudes but random relative phases.

QVNS quantum-accurate signals are used to characterize the amplitude-frequency response and the 

nonlinear behavior of electronic components, such as the multiple amplifier stages and the analog-todigital-converters.

S. P. Benz, J. M. Martinis, S. W. Nam, W. L. Tew, and D. R. White, “A new approach to Johnson noise 

thermometry using a Josephson quantized voltage source for calibration,” in: Proceedings of 

TEMPMEKO 2001, the 8th International Symposium on Temperature and Thermal Measurements in 

Industry and Science, B. Fellmuth, J. Seidel, and G. Scholz, Eds., Berlin: VDE Verlag, April 2002, vol. 

19, pp. 37-44.
382

Similar to the Watt balance that compares mechanical and electrical power to measure Plank’s constant h 

and the kilogram, the NIST QVNS-JNT system measures very small electrical noise in a resistor that 

resides in water triple point cell. “Johnson noise” is created by the random motion of electrons and the 

generated noise voltage is directly proportional to temperature. The electronic devices measuring the 

noise are calibrated with voltage signals synthesized by the QVNS, whose accuracy derives from the 

quantized pulses and the quantum mechanical behavior of the Josephson effect. This unique feature 

enables the JNT system to match electrical power and thermal-noise power at the triple point of water, 

and assures that JNT systems with comparable quantum-based voltages will produce identical results.
39

The Boltzmann constant relates energy to temperature for individual particles such as atoms. The 

accepted value of this constant has been based primarily on a 1988 NIST measurement performed using 

acoustic gas thermometry, with a relative standard uncertainty of less than 2 parts per million (ppm). The 

technique is highly accurate but the experiment is complex and difficult to perform. To assure that the 

Boltzmann constant can be determined accurately around the world, scientists have been repeating the 

gas-based measurements and also developing different measurements with improved uncertainty.

The first QVNS-JNT measurement of Boltzmann’s constant in 2010 found agreement with the 

conventional value to within an uncertainty of 12 parts in 10^6. However, 10 days of continuous signal 

integration was required to reduce the statistical uncertainty (cross-correlate out the amplifier noise) to 5 

parts in 10^6. Unfortunately, there combined uncertainty was much larger due to a systematic error 

caused by variations in the measured frequency response. The measured value k/h should be independent 

of frequency (another flat spot!), as well as with respect to pulse amplitude and resistor value. In 2015, 

NIM’s (National Institute of Metrology, China) QVNS-JNT system yielded a measurement with a 

combined uncertainty of 4 parts in 10^6 after 34 days of integration. AIST’s (National Institute of 

Advanced Industrial Science and Technology, Japan) JNT system uses quantum-based voltage waveforms 

synthesized by a direct digital synthesizer. Their system has a achieved a statistical measurement 

uncertainty of 9 parts in 10^6 in 7 days of integration. Improvements are being made to all three system 

with the expectation to produce reduced measurement uncertainties by July 2017, with the goal of a 

combined uncertainty of 3 parts in 10^6.

S.P. Benz, et al., “An Electronic Measurement of the Boltzmann Constant,” Metrologia, vol. 48, pp. 142-

153, March 2011.

Jifeng Qu, S. P. Benz, A. Pollarolo, H. Rogalla, W. Tew, R. White, and Kunli Zhou, “Improved electronic 

measurement of the Boltzmann constant by Johnson noise Thermometry,” Metrologia, vol. 52, pp. 441-

451, June 2015. stacks.iop.org/Met/50/441, doi:10.1088/0026-1394/50/5/441

C. Urano et al., “Johnson Noise Thermometry Based on Integrated Quantum Voltage Noise Source,"

IEEE Trans. Appl. Supercond., vol. 26, no. 3, pp. 1800305-5, Apr. 2016.
40

The QVNS is a low-voltage realization of the JAWS. Since the amplitude of the pseudo-noise waveforms 

are small (<1 μV peak), the QVNS only requires a few Josephson junctions, typically 8 junctions are 

used. A typical 1cm x 1 cm chip consists of two 4-junction arrays connected in series to a common 

ground. Two sets of three-wire leads transmit the grounded differential signal to each of the two crosscorrelation measurement channels.
41

The instrument is simpler and more compact than that of other methods for measuring the Boltzmann 

constant. This picture shows the measurement configuration inside an rf shielded room, including (1) the 

thermoelectric cooler containing the triple point that holds the sense resistor, (2) the 30 L liquid helium 

storage dewar containing the cryoprobe that holds the QVNS (pulse bias source is external to the room), 

and (3) the cross-correlation measurement system, which is powered by sets of Li-ion batteries alternately 

switched between charging and operation.

A. Pollarolo, H. Rogalla, A. E. Fox, K. J. Coakley, W. L. Tew, and S. P. Benz, "Improved spectra 

aberration in Johnson noise thermometry," 30th Conference on Precision Electromagnetic Measurements 

(CPEM 2016) Digest, presented 10–15 July 2016, Ottawa, Canada, pp. 331-2. DOI:

10.1109/CPEM.2016.7540777.
42

In conclusion, the Josephson effect has played an important role in creating quantum-based voltage 

standards. The perfectly quantized pulses produced by Josephson junction, combined with the zeroresistance properties of superconducting wires and enabled the development of quantum-based voltage 

standards. Josephson voltage standards have successfully replaced the electrochemical cell as the dc 

standard for dc voltage and have demonstrated measurement systems with improved performance for ac 

voltage, power, impedance and primary thermometry.
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Thank you from our Superconductive Electronics Group in Boulder, Colorado.