Cryogenic Current Comparator Research Articles

High Inductance Cryogenic Current Comparators for Beamlines

High Inductance Cryogenic Current Comparators for Beamlines

Development and implementation of an automated four-terminal-pair Josephson impedance bridge

The four-terminal-pair impedance bridge using pulse-driven Josephson voltage standards at PTB has been fully automated. The same bridge configuration was employed to determine R:R and C:C ratios over the frequency range between 53 Hz to 50 kHz. Only minor changes are needed to cover this large frequency range: amplifiers to increase the sensitivity of the current detections for low frequencies and signal generators with higher resolution at high frequencies to reach 50 kHz. Furthermore, the bridge can be operated for quadrature R:(1/ωC) measurements. The combined standard uncertainties (k = 1) for the new bridge were evaluated for all operating frequencies. They reach 2 nF F−1 and 4 nΩ Ω−1 at 1233.15 Hz. At this frequency, the 10 nF:10 nF ratio matched the ratio of PTB’s bridge employing inductive voltage dividers within 1 nF F−1 ± 3 nF F−1 (k = 1). Over 45 days, the 10 nF:10 nF ratio deviated less than −2 nF F−1 ± 3 nF F−1 (k = 1). The 12.9 kΩ:10 kΩ ratio at 53 Hz differed −2 nΩ Ω−1 ± 5 nΩ Ω−1 (k = 1) from the DC ratio measured by the PTB’s cryogenic current comparator bridge. Using a 12.9 kΩ resistance standard and a graphene AC quantum Hall resistance, the 10 nF:10 nF ratios derived from quadrature measurements agreed with the PTB’s inductive voltage divider bridge better than 9 nF F−1 ± 13 nF F−1 (k = 1).

On the calibration of DC resistance ratio bridges

Current comparator bridges are employed for the realization of the resistance scale from the quantum Hall effect in several National Metrology Institutes and calibration centers. Quantum resistance standards under development, based on novel materials and tabletop dry cryostats, make the more achievable DC current comparator bridges (DCCs) a viable alternative to the more accurate but more expensive cryogenic current comparator bridges (CCCs). A DCC ratios’ calibration against a reference CCC is a straightforward way to improve the DCC’s performances and the resistance scale overall accuracy.The paper reports the calibration results of two DCCs on the ratios employed in a 1Ω to 10kΩ resistance scale traceable to a 12.906kΩ quantized Hall resistance, showing a good reproducibility and stability of the DCC readings over the measurement period and supporting the possibility of a DCC errors’ correction and of a realization of the primary resistance scale at the 10-8 level.

Precision measurement of an electron pump at 2 GHz; the frontier of small DC current metrology

A well-characterised sample of silicon tunable-barrier electron pump has been operated at a frequency of 2 GHz using a custom drive waveform, generating a pump current of 320 pA. Precision measurements of the current were made as a function of pump control parameters, using a blind protocol, over a 7 week campaign. The combined standard uncertainty for each h measurement was in the range parts per million (ppm). The pump current exhibits a plateau along the exit gate voltage flat to approximately 0.15 ppm, but offset from ef by 0.2 ppm. This offset may be a sign of errors in the current traceability chain, indicating a limit to the accuracy of small current scaling using existing methods based on cryogenic current comparators.

Performance and Stability Assessment of Graphene-Based Quantum Hall Devices for Resistance Metrology

For more than three decades, GaAs/AlGaAs quantum Hall (QH) devices are being used as standards for the realization of the dc resistance unit ohm. Recently, the outstanding performance of graphene-based quantum Hall resistance (QHR) devices signifies an immense potential for a transition from GaAs to graphene-based devices in the field of resistance and also impedance metrology, with equally good accuracy. The recent developments in epitaxial graphene (EG) quality and fabrication of EG-based doped QHR devices and their improved performance tested in several national metrology institutes (NMIs) all over the world have demonstrated a more user-friendly dissemination of the unit ohm since they can be operated at relatively low magnetic fields and higher temperatures in comparison to existing GaAs-based devices. In this work, we have extensively tested the temporal stability of the magneto-transport properties of our graphene QH devices fabricated in the PTB and the resistance quantization performance by means of repeated high-accuracy cryogenic current comparator (CCC) measurements with several devices. Together with interlaboratory comparisons between NMI’s, the performance and stability assessment demonstrate the readiness of the technology for calibration purposes in resistance metrology.

Influence of Mechanical Deformations on the Performance of a Coaxial Shield for a Cryogenic Current Comparator

This paper studies the impact of mechanical deformations on the performance of a coaxial-type cryogenic current comparator (CCC). Such deformations may become a concern as the size of the CCC increases (e.g. when used as a diagnostic device in a particle accelerator facility involving beamlines with a large diameter). In addition to static deformations, this paper also discusses the effect of mechanical vibrations on the CCC performance.

Precise high resistance comparison between the NMIJ traveling dual source bridge and the NIST adapted Wheatstone bridge

A precise high resistance comparison was performed between the traveling dual source bridge developed by the National Metrology Institute of Japan (NMIJ) and the adapted Wheatstone bridge of the National Institute of Standards and Technology (NIST) from 10 MΩ to 100 TΩ at NIST. The NMIJ traveling bridge was shipped to NIST Gaithersburg and was installed right next to the NIST bridge and these bridges alternately measured the resistance ratio of the high resistance standards, without moving the location of the resistors inside the temperature controlled air-bath. Having the bridges and resistance standards in the same location for the comparison decreased the transportation and temperature coefficient effects on the resistance standards, contributing to the excellent agreement of the measured values. The NMIJ traveling bridge used an 8.5-digit digital multimeter and a relay switch box to determine a resistance ratio by measuring the ratio of the voltages applied to the resistors. The comparison was started from 10 MΩ based on the same 1 MΩ standard resistor calibrated using a NIST two-terminal cryogenic current comparator bridge, and standard resistors from 10 MΩ to 100 TΩ were calibrated by repeating 10:1 scaling measurements with both systems. Excellent agreement was obtained within the uncertainty of all resistance ranges and the difference between both systems was less than 1 μΩ Ω−1 up to 1 TΩ and the degrees of equivalence for 10 TΩ and 100 TΩ were less than 6 μΩ Ω−1.

Commissioning of the Cryogenic Current Comparator (CCC) at CRYRING

Commissioning of the Cryogenic Current Comparator (CCC) at CRYRING

Application Driven Optimization of Cryogenic Current Comparators (CCC) for Beam Storage Rings

Non-destructive measurements of nA beam currents in particle beam storage rings by detecting the azimuthal magnetic field generated by moving charged particles with a Cryogenic Current Comparator (CCC) are well established. The detection of beam currents with small amplitudes with a CCC in a storage ring demands a high slew rate which is caused by the rapid change of the beam current exceeding the operational limit of the SQUID in flux-locked loop mode. Previous solutions to increase the slew rate used a LCR first-order low-pass filter were a small resistor, unfortunately, dominated the current noise of the CCC. In this work we present a novel take by adding a second resonator into the CCC which in turn allows for higher resistances of the LCR low-pass filter and therefore lower thermal current noise. A second challenge connected with this CCC approach is the residual magnetization of the highly permeable magnetic core and the resulting shielding currents in the superconducting circuits of the CCC. The timing of a storage ring in the range of minutes opens a way to reduce these DC currents using a LR high-pass filter. Using serial sub-micro ohm resistors, time constants in the hour range can be achieved to improve the stability and performance of the CCC system.

Precision measurement of single-electron current with quantized Hall array resistance and Josephson voltage

A single electron pump was incorporated with a quantum Hall resistance and a Josephson voltage for the current evaluation in the framework of Ohm’s law. The pump current of about 60 pA level was amplified by a stable amplifier with a gain of 103 to induce a Hall voltage of about 60 mV level across a 1 MΩ Hall resistance array, which was compared with the Josephson voltage. The gain of the current amplifier was calibrated with a cryogenic current comparator bridge. For two different drive frequencies and repeated thermal cycles, the comparisons demonstrated that the pump current averaged over the first plateau was equal to ef within the combined uncertainty level of 0.3 × 10−6 (k = 1).

Application of conserved thermal-noise energy model to damped resonant behavior in cryogenic current comparators.

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.

Calibration of ultrastable low-noise current amplifiers without direct use of a cryogenic current comparator

The established calibration of the transresistance of the ultrastable low-noise current amplifier (ULCA) directly involves a cryogenic current comparator (CCC). Here, we present an alternative approach based on a calibrated set of three resistors and three digital voltmeters. This approach was experimentally verified for a two-channel ULCA with nominally 1 GΩ transresistance using PTB’s travelling 12 bit CCC setup in an on-site comparison at METAS. Series of interleaved experiments included calibrations of the input and output stages of two different ULCA channels. The consistency found between the conventional calibration with PTB’s CCC and calibration with METAS’ set of three resistors—each traced to the quantum Hall resistance with METAS’ CCC—confirms that the alternative traceability chain provides valuable results. If the standard resistors are calibrated without using a CCC, the new method even opens the possibility to calibrate the ULCA without any CCC in the traceability chain involved, however, typically at the expense of increased uncertainty.

A Resistance Bridge Based on a Cryogenic Current Comparator Achieving Sub-10⁻⁹ Measurement Uncertainties

A new resistance bridge has been built at the Laboratoire national de m\'etrologie et d'essais (LNE) to improve the ohm realization in the $Syst\`eme International$ (SI) of units from the quantum Hall effect. We describe the instrument, the performance of which relies on two synchronized and noise-filtered current sources, an accurate and stable current divider and a cryogenic current comparator (CCC) having a low noise of $\mathrm{80~pA.t/Hz^{1/2}}$. The uncertainty budget for the measurement of the 100 $\Omega/(R_\mathrm{K}/2)$ ratio, where $R_\mathrm{K}$ is the von Klitzing constant, amounts to a few parts in $10^{10}$ only.

Comparison between Graphene and GaAs Quantized Hall Devices with a Dual Probe.

A graphene quantized Hall resistance (QHR) device fabricated at the National Institute of Standards and Technology (NIST) was measured alongside a GaAs QHR device fabricated by the National Research Council of Canada (NRC) by comparing them to a 1 kΩ standard resistor using a cryogenic current comparator. The two devices were mounted in a custom developed dual probe that was then assessed for its viability as a suitable apparatus for precision measurements. The charge carrier density of the graphene device exhibited controllable tunability when annealed after Cr(CO)3 functionalization. These initial measurement results suggest that making resistance comparisons is possible with a single probe wired for two types of quantum standards - GaAs, the established material, and graphene, the newer material that may promote the development of more user-friendly equipment.

Calibrating Ultrastable Low-Noise Current Amplifiers of the Second Generation With a Cryogenic Current Comparator

Input and output stages of the second generation of ultrastable low-noise current amplifiers can be conveniently calibrated by means of a cryogenic current comparator. The uncertainty achievable for measurement durations of less than 2 h makes our calibration setup a helpful tool for the selection of hardware in the development of instrumentation tailored to meet the requirements of special applications.

Graphene Devices for Tabletop and High-Current Quantized Hall Resistance Standards.

We report the performance of a quantum Hall resistance standard based on epitaxial graphene maintained in a 5-T tabletop cryocooler system. This quantum resistance standard requires no liquid helium and can operate continuously, allowing year-round accessibility to quantized Hall resistance measurements. The ν = 2 plateau, with a value of R K/2, also seen as R H, is used to scale to 1 kΩ using a binary cryogenic current comparator (BCCC) bridge and a direct current comparator (DCC) bridge. The uncertainties achieved with the BCCC are such as those obtained in the state-of-the-art measurements using GaAs-based devices. BCCC scaling methods can achieve large resistance ratios of 100 or more, and while room temperature DCC bridges have smaller ratios and lower current sensitivity, they can still provide alternate resistance scaling paths without the need for cryogens and superconducting electronics. Estimates of the relative uncertainties of the possible scaling methods are provided in this report, along with a discussion of the advantages of several scaling paths. The tabletop system limits are addressed as are potential solutions for using graphene standards at higher currents.

Interlaboratory Nanoamp Current Comparison With Subpart-Per-Million Uncertainty

An ultrastable low-noise current amplifier (ULCA) has been transferred between two laboratories, NPL and PTB, four times, with three of the transfers yielding a relative change in the trans-resistance gain of less than $2 \times 10^{-7}$. This is a new bench-mark for inter-laboratory transfer of small current. We describe in detail the use of a cryogenic current comparator to calibrate the ULCA at NPL, and the use of the ULCA to measure $1$ G$\Omega$ resistors with relative uncertainties at the $10^{-7}$ level.

Quantum Hall devices for the primary resistance standard based on the GaAs/AlxGa1−x As heterostructure

Quantum Hall devices for primary resistance metrology based on the GaAs/Al[Formula: see text]Ga[Formula: see text]As heterostructure were fabricated and compared with the devices from international metrology organization International Bureau of Weights and Measures (BIPM) by calibrating the same 100 [Formula: see text] transfer standard resistor with a cryogenic current comparator. Relative deviation between NIM-made device NIM-C1 and BIPM-made device BIPM-1 was −4.49 parts in 109 with an uncertainty of 3.63 parts in 109 which indicated NIM-C1 satisfied the requirement for the primary resistance standard.

Numerical analysis of a folded superconducting coaxial shield for cryogenic current comparators

This paper presents a new shield configuration for cryogenic current comparators (CCCs), namely the folded coaxial geometry. An analytical model describing its shielding performance is first developed, and then validated by means of finite element simulations. Thanks to this model, the fundamental properties of the new shield are highlighted. Additionally, this paper compares the volumetric performance of the folded coaxial shield to the one of a ring shield, the latter being installed in many CCCs for measuring particle beam currents in accelerator facilities.

Noise-optimized ultrastable low-noise current amplifier.

We have developed a noise-optimized ultrastable low-noise current amplifier (ULCA) aimed at reducing the uncertainty at low currents. It involves a thin-film resistor network with 6.75 GΩ at the high-ohmic path which reduces the noise level to 1.6 fA/Hz. Noise investigations as well as short-term and long-term stability studies were carried out. The stability of the input current gain was measured using a cryogenic current comparator at ±6.1 nA. Methods for investigating the measurement accuracy at low input currents of about 100 pA at a level of below one part in 107 are introduced and experimentally verified. The performance of the noise-optimized ULCA is compared with that of the standard variant introduced in 2014. It is shown that the reduced noise floor is achieved without impairing the stability of the transresistance.