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Physical review. B, Solid state

ac-Josephson-Effect Determination of e h : A Standard of Electrochemical Potential Based on Macroscopic Quantum Phase Coherence in Superconductors

Thomas F. Finnegan, Arnold M. Denenstein, D. N. Langenberg

Published Sep 1, 1971• 66 citations
Publisher

Abstract

An ac-Josephson-effect determination of $\frac{e}{h}$ with significantly improved accuracy is reported. The precision of the measurement is determined by uncertainties associated with the comparison of a Josephson-device voltage with the emf of an electrochemical-standard-cell voltage reference and is about 3 parts in ${10}^{8}$. This precision was made possible by use of Josephson devices at voltages above 10 mV and design and construction of two special voltage-comparator instruments. The fabrication and operation of the Josephson devices and the design and performance of the voltage comparators are discussed. The 3/${10}^{8}$ precision represents the precision with which a drift-free and readily reproducible Josephson voltage standard can be realized in practice using the techniques developed for these experiments. The accuracy of the final result is about 12 parts in ${10}^{8}$ and is determined primarily by uncertainties associated with the stability of the local electrochemical voltage standard and with establishment of the relationship between the local volt and the volt maintained by the U. S. National Bureau of Standards. Significant improvements in the maintenance of the local-voltage standard which contributed to reduction of the final uncertainty to this value are discussed. During the course of the experiments, the Josephson frequency-voltage relation was shown experimentally to be independent of magnetic field, temperature, and Josephson-device bias voltage or induced step number to within the accuracy of the final result. The final experimental result and its one-standard-deviation uncertainty are $\frac{2e}{h}=(483.593718\ifmmode\pm\else\textpm\fi{}0.000060)\frac{\mathrm{MHz}}{\ensuremath{\mu}{V}_{\mathrm{NBS}69}}$ (0.12 ppm) referred to the volt as maintained by the U. S. National Bureau of Standards after January 1, 1969. This result is in excellent agreement with the earlier, less accurate result of Parker, Langenberg, Denenstein, and Taylor, which played an important role in the 1969 adjustment of the fundamental physical constants by Taylor, Parker, and Langenberg. It is in reasonable agreement with values recently reported by several other groups. The significantly improved accuracy of the present result makes possible a small improvement in the accuracy of the derived value of the fine structure constant and clears the way for a larger improvement through more accurate determination of the proton gyromagnetic ratio.

DOI
10.1103/physrevb.4.1487

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Quantized currents at 2ef - studying the potential of dual Shapiro steps for a quantum current standard

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Electrical quantum metrology using superconducting circuits relies on phase synchronization effects of Josephson oscillations with ac signals, resulting in equidistant voltage steps and forming the basis of today’s voltage standards. Because charge and phase are conjugate variables, the dual effect of equidistant current steps should also exist and was indeed predicted theoretically. It relies on so-called Bloch oscillations, which are oscillations of voltage occurring when a current-biased Josephson junction is embedded in an environment with characteristic impedance larger than the superconducting resistance quantum h/4e^2. In addition, Josephson junctions of lateral size on the order of tens of nm are necessary, such that their Josephson and charging energy are approximately equal. Synchronizing such Bloch-oscillations with an ac signal completes the duality with Shapiro steps, and results in the occurrence of steps in IV-measurements at I=2ef with e being the elementary charge, and f the frequency of the external ac signal. To emphasize the duality with Shapiro (voltage) steps, such current steps are called dual-Shapiro steps. Together with the established standards for voltage and resistance, a new standard for current based on dual-Shapiro steps would relate the ampere, volt and ohm through fundamental constants and frequency. If successfully realized with metrological precision this would close the quantum metrological triangle and might even enable the combination of all three electric quantum relations in one single device. Here we show our efforts towards the realization of quantized currents with metrological applicability. Based on advances in fabrication technology and measurement capabilities, we demonstrate quantized current steps up to I≈2 nA by synchronizing Bloch oscillations with external ac signals up to 6 GHz [1,2]. In addition, we demonstrate a pulsed driving scheme resulting in an asymmetric pattern of dual-Shapiro steps featuring increased differential resistance [2]. Finally, we discuss the effects limiting the precision of our quantized current steps and present our efforts for tackling them. [1] F. Kaap et al., “Synchronization of Bloch Oscillations in a Strongly Coupled Pair of Small Josephson Junctions: Evidence for a Shapiro-like Current Step,“ Phys. Rev. Lett. 132, 027001, 2024. [2] F. Kaap et al., “Demonstration of dual Shapiro steps in small Josephson junctions,“ Nature Communications 15, 8726, 2024.

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Josephson junctions in charge and phase picture Theory and applications

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•Nov 9, 2004•0 citations
An ac-Josephson-effect determination of eh\frac{e}{h}he​ with significantly improved accuracy is reported. The precision of the measurement is determined by uncertainties associated with the comparison of a Josephson-device voltage with the emf of an electrochemical-standard-cell voltage reference and is about 3 parts in 108{10}^{8}108. This precision was made possible by use of Josephson devices at voltages above 10 mV and design and construction of two special voltage-comparator instruments. The fabrication and operation of the Josephson devices and the design and performance of the voltage comparators are discussed. The 3/108{10}^{8}108 precision represents the precision with which a drift-free and readily reproducible Josephson voltage standard can be realized in practice using the techniques developed for these experiments. The accuracy of the final result is about 12 parts in 108{10}^{8}108 and is determined primarily by uncertainties associated with the stability of the local electrochemical voltage standard and with establishment of the relationship between the local volt and the volt maintained by the U. S. National Bureau of Standards. Significant improvements in the maintenance of the local-voltage standard which contributed to reduction of the final uncertainty to this value are discussed. During the course of the experiments, the Josephson frequency-voltage relation was shown experimentally to be independent of magnetic field, temperature, and Josephson-device bias voltage or induced step number to within the accuracy of the final result. The final experimental result and its one-standard-deviation uncertainty are 2eh=(483.593718\ifmmode±\else\textpm\fi0.000060)MHz\ensuremathμVNBS69\frac{2e}{h}=(483.593718\ifmmode\pm\else\textpm\fi{}0.000060)\frac{\mathrm{MHz}}{\ensuremath{\mu}{V}_{\mathrm{NBS}69}}h2e​=(483.593718\ifmmode±\else\textpm\fi0.000060)\ensuremathμVNBS69​MHz​ (0.12 ppm) referred to the volt as maintained by the U. S. National Bureau of Standards after January 1, 1969. This result is in excellent agreement with the earlier, less accurate result of Parker, Langenberg, Denenstein, and Taylor, which played an important role in the 1969 adjustment of the fundamental physical constants by Taylor, Parker, and Langenberg. It is in reasonable agreement with values recently reported by several other groups. The significantly improved accuracy of the present result makes possible a small improvement in the accuracy of the derived value of the fine structure constant and clears the way for a larger improvement through more accurate determination of the proton gyromagnetic ratio.
Electrical quantum metrology using superconducting circuits relies on phase synchronization effects of Josephson oscillations with ac signals, resulting in equidistant voltage steps and forming the basis of today’s voltage standards. Because charge and phase are conjugate variables, the dual effect of equidistant current steps should also exist and was indeed predicted theoretically. It relies on so-called Bloch oscillations, which are oscillations of voltage occurring when a current-biased Josephson junction is embedded in an environment with characteristic impedance larger than the superconducting resistance quantum h/4e^2. In addition, Josephson junctions of lateral size on the order of tens of nm are necessary, such that their Josephson and charging energy are approximately equal. Synchronizing such Bloch-oscillations with an ac signal completes the duality with Shapiro steps, and results in the occurrence of steps in IV-measurements at I=2ef with e being the elementary charge, and f the frequency of the external ac signal. To emphasize the duality with Shapiro (voltage) steps, such current steps are called dual-Shapiro steps. Together with the established standards for voltage and resistance, a new standard for current based on dual-Shapiro steps would relate the ampere, volt and ohm through fundamental constants and frequency. If successfully realized with metrological precision this would close the quantum metrological triangle and might even enable the combination of all three electric quantum relations in one single device. Here we show our efforts towards the realization of quantized currents with metrological applicability. Based on advances in fabrication technology and measurement capabilities, we demonstrate quantized current steps up to I≈2 nA by synchronizing Bloch oscillations with external ac signals up to 6 GHz [1,2]. In addition, we demonstrate a pulsed driving scheme resulting in an asymmetric pattern of dual-Shapiro steps featuring increased differential resistance [2]. Finally, we discuss the effects limiting the precision of our quantized current steps and present our efforts for tackling them. [1] F. Kaap et al., “Synchronization of Bloch Oscillations in a Strongly Coupled Pair of Small Josephson Junctions: Evidence for a Shapiro-like Current Step,“ Phys. Rev. Lett. 132, 027001, 2024. [2] F. Kaap et al., “Demonstration of dual Shapiro steps in small Josephson junctions,“ Nature Communications 15, 8726, 2024.
The past few decades have witnessed great progress being made from the first voltage standards based on arrays of Josephson junctions. Continuous improvements in the fabrication process have increased the quality and “user-friendliness” of these superconducting circuits. Combined with the improvements in measuring electronics, the range of applications of Josephson-based measurements with unmatched precision has extended from DC into AC voltage metrology for signal frequencies up to 500 kHz. In this poster we will present several Josephson-based measurement systems developed for metrology applications. Two versions of quantum AC standards will be used as Josephson references: Programmable Josephson Voltage Standards (PJVS), which are based on serial arrays with up to 300,000 Josephson junctions, and pulse-driven arrays with more than 50,000 junctions, typically referred to as Josephson Arbitrary Waveform Synthesizers (JAWS). PJVS can reach amplitudes of up to 80 V, while pulse-driven arrays can reach up to 1 V or even 4 V. The advantage of pulse-driven Josephson voltage standards is that they are ideally suited as quantum-based voltage synthesizers for arbitrary waveforms or sine waves with high spectral purity. Therefore, they can be used directly to characterize or calibrate ADCs. In addition, JAWS are particularly useful in Josephson impedance bridges, which perform automated impedance calibrations at the 10-9 uncertainty level over a wide frequency range from 50 Hz to 80 kHz in a single bridge. We will further show how PJVS are used in commercial quantum voltmeters for DC and AC voltages and are typically used as quantum voltage references in measurement systems. Using differential sampling based on PJVS, uncertainties at the level of a few parts in 108 for frequencies up to the kHz range can be achieved. Such quantum-based AC voltage calibrations are at least 30 times faster than conventional AC-DC transfer and offer even better uncertainties. This idea has been quickly adopted by many National Metrology Institutes to establish such systems for AC voltage calibrations. As an example, the BIPM will now start worldwide onsite comparisons to ensure the uniformity of the new method which we introduced in 2006. But developments continue. Recently, a sub-sampling technique was used to extend the frequency range of the AC quantum voltmeter to up to 100 kHz with uncertainties below 5 parts in 106. In addition, a novel method, also for differential sampling, enables the measurement of arbitrary waveforms and the calibration of specific tones. Our poster will provide an overview of these Josephson-based metrological applications and present the latest developments from this fast-developing area.
The advancement of quantum metrology is intrinsically linked to the development of nanoelectronic and quantum devices. The Programmable Josephson Voltage Standard (PJVS), a system comprising thousands of superconducting Josephson junctions with tunnel barriers on the nanoscale, provides a fundamental quantum-based AC voltage reference. However, extending this quantum traceability to harmonic power measurements, essential for modern power systems with extensive power electronics, remains a significant challenge. This work demonstrates a high-accuracy harmonic power standard by leveraging the unique quantum properties of a nano-fabricated PJVS array. We introduce a time-division calibration scheme where the precise voltage steps of the PJVS are used to calibrate a high-performance dual-channel analog-to-digital converter (ADC). This method bypasses the need for complex synchronous sampling and heavy computational algorithms, relying instead on the intrinsic accuracy of the Josephson quantum voltage. The system achieves a measurement uncertainty of 14 × 10 ×6 ( k = 2) for fundamental power and 50 × 10 −6 ( k = 2) for harmonic power up to the 60th order. Comparative tests with national primary standards show a maximum deviation of only 6 × 10 −6 for harmonic power metrology but also serves as a compelling demonstration of a practical, high-precision application for superconducting nanoelectronic devices, bridging the gap between quantum standards and industrial measurement needs.
Recent advances in circuit design and fabrication of superconducting integrated circuits have enabled us to demonstrate an ac Josephson voltage standard (ACJVS) that generates both ac and dc waveforms up to 242-mV peak voltage. Using a Fast Fourier Transform spectrum analyzer and an ac-dc transfer standard, we characterize ACJVS operating margins by performing "flat-spot" measurements at the level of a part in 10/sup 6/ for all eight bias parameters. By verifying that every bias parameter has a "flat-spot" (i.e., a range of bias values over which the measured ACJVS output is precisely constant), we demonstrate that all Josephson junctions on the chip are operating properly.
The DC voltage across a Josephson junction is exactly determined by the number of single flux quanta Φ0passing the junction per second. By locking this flux train to an external sinusoidal microwave with the frequency f or a pulse train with the pulse rate f in such a way that one flux quantum is transferred per microwave period or per pulse respectively, the junction DC voltage becomes V=Φ0f in the simplest case. The precision of V is only determined by the uncertainty of the frequency control. As the output voltage is relatively small (V=140μV for f=70GHz), large series arrays of n Josephson junctions must be used to increase the voltage to practical levels V=nΦ0f. With a sinusoidal 70 GHz microwave drive and series arrays of up to 14000 SIS tunnel junctions modern DC voltage standards were developed in the past which may reach a reproducibility of a few parts in 10-10. These standards are commercially available and form the basis of the legal voltage metrology of most of the national laboratories worldwide. Because the reference voltages of these standards are widely overlapping it is difficult to rapidly adjust the desired voltage. It was therefore impossible to use these quantum voltmeters for the precise analysis of AC voltages. For this purpose the arrays had to be modified in many respects. The direct way to generate arbitrary Josephson waveforms V(t) is to rapidly alter the frequency f(t) with respect to the desired waveform V(t)=nf(t)Φ0. It requires a precise flux transfer control over a very wide frequency range.
Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.