In this article, we present a range of quantum-based measurement systems that we have developed for applications in the field of metrology. The core of these systems are Josephson arrays, which we manufacture in our clean room. Pulse-driven Josephson voltage standards are used in Josephson impedance measuring bridges. Due to their flexibility automated impedance calibrations can be performed over a wide frequency range from 50 Hz to 50 kHz in a single bridge. At 1233 Hz uncertainties of parts in 109 for 1:1-capacitance ratios with 10 nF are realised – comparable to world-class IVD-based impedance bridges. Programmable Josephson voltage standards allow us to calibrate DC and AC voltages with uncertainties at the level of parts in 1010, few parts in 108 (up to kHz range), and below 5 parts in 106 up to 100 kHz, respectively.

This paper introduces a four-terminal-pair impedance bridge based on pulse-driven Josephson junctions arrays which is designed to link any kind of impedance to the quantized Hall resistance. The unique features of the quantized Hall resistance in a multiple series connection allows to dispense a combining network and leads to a compact and simple design of the whole setup. Moreover, the low noise of a quantized Hall resistance reduces the measurement time compared to resistance standards at room temperature which is essential for the characterization of quantum Hall devices in the AC regime. A first measurement campaign confirmed the expected low noise of 1.82 nV/root Hz for a link to a 10 nF capacitance standard. The repeatability of the bridge was found to be few parts in 10(8). Capacitance and resistance standards were measured at 1233.15 Hz against graphene based quantum Hall resistance devices.

The KArlsruhe TRItium Neutrino (KATRIN) experiment, which aims to make a direct and model-independent determination of the absolute neutrino mass scale, is a complex experiment with many components. More than 15 years ago, we published a technical design report (TDR) [1] to describe the hardware design and requirements to achieve our sensitivity goal of 0.2 eV at 90% C.L. on the neutrino mass. Since then there has been considerable progress, culminating in the publication of first neutrino mass results with the entire beamline operating [2]. In this paper, we document the current state of all completed beamline components (as of the first neutrino mass measurement campaign), demonstrate our ability to reliably and stably control them over long times, and present details on their respective commissioning campaigns.

A novel four-terminal pair impedance bridge combined with a quantum Hall resistor will be presented. The impedance bridge is based on pulse-driven Josephson arrays. A very simple setup is possible due to the triple-series connection of the quantum Hall resistor that renders combining networks superfluous. This combination of the two well-known macroscopic quantum effects presents a unique possibility for the realization of electrical units. Moreover, the Josephson bridge can be used to precisely investigate the plateau shape of quantum Hall devices in the AC regime.

This paper reports on the comparison of two Josephson arbitrary waveform synthesizers for frequencies up to 500 kHz. Both independent pulse-driven Josephson arrays produce a 10 mV RMS sinusoidal voltage. They are alternately connected to an analog-to-digital converter which serves as a transfer standard. The setup is capable to of synthesizing quantum-based waveforms using two different pulse-bias techniques. We use the Zero-Compensation method and a two-pole high-pass filter structure in the pulse-bias configuration of one system (the reference) to minimize the amplitude error for signal frequencies up to 500 kHz. Consequently, we are able to directly detect the high-frequency voltage errors in the other system (the device under test). The setup is used to measure differences between both systems, and the influence of parameter variation on the results with Type A uncertainties of 0.4 mu V/V (k = 1) in measurement times of 60 s. We find that the dominant sources of deviations above 10 kHz can be traced to the influence of the output cabling and the pulse bias on the synthesized voltage signal. Our analysis explains the origin and the reduction of these high-frequency voltage errors.

This paper reports on a comparison of two pulse-driven Josephson voltage standards using the zero compensation pulse-bias method. Each system produces a sinusoidal voltage with an RMS signal amplitude of 10 mV for signal frequencies up to 500 kHz. By comparing the results to measurements using the conventical pulse-bias method, we can evaluate the improvements in the absolute accuracy of the synthesized AC signal of each system as well as in the deviation between both systems at signal frequencies above 10 kHz.

The most common method to measure direct current high voltage (HV) down to the ppm-level is to use resistive high-voltage dividers. Such devices scale the HV into a range where it can be compared with precision digital voltmeters to reference voltages sources, which can be traced back to Josephson voltage standards. So far the calibration of the scale factors of HV dividers for voltages above 1 kV could only be done at metrology institutes and sometimes involves round-robin tests among several institutions to get reliable results. Here we present a novel absolute calibration method based on the measurement of a differential scale factor, which can be performed with commercial equipment and outside metrology institutes. We demonstrate that reproducible measurements up to 35 kV can be performed with relative uncertainties below 1 . 10(-6). This method is not restricted to metrology institutes and offers the possibility to determine the linearity of high-voltage dividers for a wide range of applications.

We report on the neutrino mass measurement result from the first four-week science run of the Karlsruhe Tritium Neutrino experiment KATRIN in spring 2019. Beta-decay electrons from a high-purity gaseous molecular tritium source are energy analyzed by a high-resolution MAC-E filter. A fit of the integrated electron spectrum over a narrow interval around the kinematic end point at 18.57 keV gives an effective neutrino mass square value of (-1.0_{-1.1}^{+0.9})  eV^{2}. From this, we derive an upper limit of 1.1 eV (90% confidence level) on the absolute mass scale of neutrinos. This value coincides with the KATRIN sensitivity. It improves upon previous mass limits from kinematic measurements by almost a factor of 2 and provides model-independent input to cosmological studies of structure formation.

The KATRIN experiment is designed to determine the absolute neutrino mass scale with a sensitivity of 200 meV (90 % CL) by measuring the electron energy spectrum close to the endpoint of molecular tritium beta decay. Electrons from a high-intensity gaseous tritium source are guided by a strong magnetic field of a few T to the analyzing plane of the main spectrometer where an integral energy analysis takes place in a low field region (B<0.5 mT). An essential design feature to obtain adiabatic electron transport through this spectrometer is a large volume air coil system surrounding the vessel. The system has two key tasks: to adjust and fine-tune the magnetic guiding field (Low Field Correction System), as well as to compensate the distorting effects of the earth magnetic field (Earth Field Compensation System). In this paper we outline the key electromagnetic design issues for this very large air coil system, which allows for well-defined electron transmission and optimized background reduction in the KATRIN main spectrometer.

This paper describes the characterization of a quantum voltage noise source (QVNS) based on pulse-driven Josephson-arrays for frequencies up to 200 kHz. The QVNS synthesizes a voltage noise reference which is used to calibrate the electronics of a Johnson noise thermometer (JNT). To realize an “electronic Kelvin” with measurement uncertainty at μK/K -level, we investigated the frequency-dependent voltage difference between two pulse-driven Josephson Arrays, each one producing a 10 mV RMS sinusoidal voltage.

Pulse-driven Josephson arrays successfully demonstrated their high potential for impedance metrology in the last years. With their high spectral purity and fundamental accuracy, they are perfectly suited for impedance measurements over the whole complex plane. PTB's two-terminal impedance bridge is equipped with new electronics to extend the frequency range, to increase the signal amplitude and to simplify the setting of the phase angle. A 1:1 ratio measurement of 10 nF capacitance standards has been carried out between 246 Hz and 40 kHz at a signal amplitude of 75 mV (RMS). The value of a 10 nF capacitance standard is traced back to the ac quantum Hall resistor at PTB using 100 mV (RMS) signal amplitude.

A recently introduced coherent sub-sampling technique has been implemented to extend the frequency range of our AC quantum voltmeter up to 100 kHz. The measurement results are compared with differential sampling for frequencies up to 10 kHz. Above 3 kHz all preliminary results show a deviation from nominal values which increases quadratic with frequency. Possible error sources and corrections are discussed.

We present a method for the voltage ratio calibration of inductive voltage dividers using quantum accurate pulse-driven Josephson standards. The inductive voltage divider calibration is carried out at 497 Hz with RMS amplitudes of 40 mV and 100 mV and is compared with conventional bootstrapping calibrations performed at 1 V. In these preliminary measurements, the new calibration method reached similar in-phase uncertainties as the bootstrapping method, despite the large difference in input voltages.

The KATRIN experiment aims to determine the effective electron neutrino mass with a sensitivity of \({0.2}{\hbox { eV/c}^{2}}\) (%90 CL) by precision measurement of the shape of the tritium \(\upbeta \)-spectrum in the endpoint region. The energy analysis of the decay electrons is achieved by a MAC-E filter spectrometer. A common background source in this setup is the decay of short-lived isotopes, such as \({}^{\text {219}}\text {Rn}\) and \({}^{\text {220}}\text {Rn}\), in the spectrometer volume. Active and passive countermeasures have been implemented and tested at the KATRIN main spectrometer. One of these is the magnetic pulse method, which employs the existing air coil system to reduce the magnetic guiding field in the spectrometer on a short timescale in order to remove low- and high-energy stored electrons. Here we describe the working principle of this method and present results from commissioning measurements at the main spectrometer. Simulations with the particle-tracking software Kassiopeia were carried out to gain a detailed understanding of the electron storage conditions and removal processes.

In this paper the realization of a two-terminal-pair impedance bridge based on pulse-driven Josephson arrays will be presented. This bridge was used to link a 10 nF capacitance standard to the quantized Hall resistance at 1233 Hz. With pulse-driven Josephson arrays the setup for a quadrature bridge can be reduced dramatically. For the combination of the AC quantum Hall resistance and a 10 nF capacitance standard, most of the uncertainties caused by contact resistances in a two-terminal-pair definition were circumvented by a triple-series connection of the AC quantum Hall resistance. The capacitance value obtained by the new Josephson impedance bridge was compared to the results from a transformer-based ratio bridge and agrees within 1.3 parts in 10(8). Sources of systematic uncertainties were investigated and the combined relative uncertainty of the bridge was determined to be less than 1x10(-8) (k = 1) and 13.9 nFF(-1) (k = 1) for the link of the 10 nF capacitance standard.

The KATRIN experiment will probe the neutrino mass by measuring the β-electron energy spectrum near the endpoint of tritium β-decay. An integral energy analysis will be performed by an electro-static spectrometer (``Main Spectrometer''), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m3, and a complex inner electrode system with about 120 000 individual parts. The strong magnetic field that guides the β-electrons is provided by super-conducting solenoids at both ends of the spectrometer. Its influence on turbo-molecular pumps and vacuum gauges had to be considered. A system consisting of 6 turbo-molecular pumps and 3 km of non-evaporable getter strips has been deployed and was tested during the commissioning of the spectrometer. In this paper the configuration, the commissioning with bake-out at 300 °C, and the performance of this system are presented in detail. The vacuum system has to maintain a pressure in the 10−11 mbar range. It is demonstrated that the performance of the system is already close to these stringent functional requirements for the KATRIN experiment, which will start at the end of 2016.

In order to determine arbitrary impedance ratios, PTB implemented an impedance bridge based on pulse-driven Josephson arrays. The sine-waves generated by these arrays possess high spectral purity and quantum precise amplitudes. This new system allows to measure like impedance ratios (R:R or C:C) over a wide range and also to make quadrature measurements (ωRC = 1). The combination of this system with the ac quantum-Hall resistor will result in a universal and high precision impedance bridge.

The establishment at PTB of an AC Josephson voltage standard (Josephson Arbitrary Waveform Synthesizer-JAWS) based on pulse-driven Josephson arrays is focused on achieving an output voltage of at least 1 V-RMS which is required for many metrology applications. In this paper, we approached this goal by increasing the number of active junctions in two ways. Firstly, we fabricated arrays containing triple-stacked SNS-type Josephson junctions with Nb-x Si1-x as barrier material. We obtained current operation margins of about 0.2 mA with arrays of up to 9000 Josephson junctions at an rms voltage of 355 mV. Secondly, we used a new 8-channel ternary pulse pattern generator (PPG) to bias up to 8 arrays connected in series. An output voltage of V-RMS = 1006 mV(V-PP = 2.845 V) was achieved by using 8 arrays (arranged on 4 separate chips) with 63 000 junctions in total. Higher harmonics are suppressed by at least -116 dBc. The fabrication process and the experimental setup will be described, as well as experimental results that are leading towards our 1 V goal.

The KATRIN experiment will measure the absolute mass scale of neutrinos with a sensitivity of mν = 200meV/c2 by means of an electrostatic spectrometer set close to the tritium β-decay endpoint at 18.6keV. Fluctuations of the energy scale must be under control within ±60mV (±3ppm). Since a precise voltage measurement in the range of tens of kV is on the edge of current technology, a nuclear standard will be deployed additionally. Parallel to the main spectrometer the same retarding potential will be applied to the monitor spectrometer to measure 17.8-keV K-conversion electrons of 83mKr. This article describes the setup of the monitor spectrometer and presents its first measurement results.

We are developing a pulse-driven Josephson voltage standard with an 1 Vrms output voltage. On our way to the 1 V level we have already reached 307 mVrms by combining five Josephson arrays with 27,000 junctions in total. Spectrally pure sine waves are achieved for voltages up to 132 mVrms. At higher voltage we observe harmonics due to interference of compensation signals and non-linearity of the sampler. An excellent direct on-chip comparison at 22 mVrms demonstrates that perfect quantization is possible with a relative uncertainty of (1.8 ± 2.0) × 10·8 (k = 2).