Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2506.12989

The impact of parameter spread of high-temperature superconducting Josephson junctions on the performance of quantum-based voltage standards

Wen, Guanghong, Zhu, Yi, Zheng, Yingxiang, Cui, Shuhe, Wang, Ji, Yanyun Ren, Hao Li, Zhang, Guofeng, Lixing You

Published Jun 15, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum metrology based on Josephson junction array reproduces the most accurate desired voltage by far, therefore being introduced to provide voltage standards worldwide. In this work, we quantitatively analyzed the dependence of the first Shapiro step height of the junction array at 50 GHz on the parameter spread of 10,000 Josephson junctions by numerical simulation with resistively shunted junction model. The results indicate an upper limit spread of the critical current and resistance of the Josephson junctions. Specifically, to keep the maximum first Shapiro step above 0.88 mA, the critical current standard deviation, $σ$, should not exceed 25%, and for it to stay above 0.6 mA, the resistance standard deviation should not exceed 1.5%.

DOI
10.48550/arxiv.2506.12989

Related papers

The impact of parameter spreads of Josephson junctions on the performance of quantum-based voltage standards

Guanghong Wen, Yi Zhu, Y. Zheng +4 more

Quantum metrology based on Josephson junction array reproduces the most accurate desired voltage by far, therefore being introduced to provide voltage standards worldwide. In this work, we quantitatively analyzed the dependence of the first Shapiro step height of the junction array at 70 GHz on the parameter spread of 8,000 Josephson junctions with an average critical current (Ic) of 3.5 mA and an average normal state resistance (Rn) of 40 mΩ, using numerical simulations based on the resistively shunted junction (RSJ) model. The results indicate an upper limit spread of the Ic and Rn of the Josephson junctions. Specifically, to keep the maximum first Shapiro step above 0.9 mA, the Ic standard deviation, σ, should not exceed 25%, and for it to stay above 0.5 mA, the Rn deviation should not exceed 9%. This analysis specifically clarifies the required level of manufacturing process sophistication for superconducting devices to realize high-temperature superconducting (HTS) quantum-based voltage standards.

Physica C Superconductivity•Aug 19, 2026•0 citations

Numerical analysis of Josephson junction arrays for multi-order quantum voltage steps

Paolo Durandetto

Abstract The dynamics of overdamped Josephson junctions under varying microwave-driving conditions have been studied through numerical simulations using the resistively-shunted junction model, with a focus on primary voltage metrology applications, where a significantly high number of series-connected junctions and stringent uniformity of their electrical parameters are required. The aim is to determine the optimal junction characteristics and external microwave (rf) parameters that maximize the width of quantum voltage levels (Shapiro steps) from order n = 0 to n > 1. Both the rf and dc power requirements, along with the junction parameter spread and power attenuation, are analyzed as key factors that need to be optimized for improved performance of the quantum device. This work aims to advance the development of next-generation programmable Josephson voltage standards with logic architectures that surpass the conventional binary and ternary codifications used in present quantum voltage arrays, while significantly reducing the overall number of junctions as well as the number of sub-arrays and bias lines. Existing technologies exploiting n = 0 and n = ± 1 voltage steps are first discussed and analyzed to verify the validity of the simulation model. They are then further investigated to extend their usability with multi-order quantum steps for n up to 3. From the simulation results, it follows that present junction technologies may be employed with no modifications for the simultaneous operation of quantum steps up to n = 2, although optimal power efficiency would require a retrimming of the junction’s electrical parameters. On the contrary, extending the highest step order to n = 3 strictly requires the junction’s characteristic parameters to be properly adjusted to maintain sustainable power levels as well as acceptable quantum-locking ranges.

arXiv:2410.07835•Superconductor Science and Technology•May 20, 2025•1 citation

Large constant voltage generated with a single array including 65 536 Nb/TiN/Nb Josephson junctions

Hirotake Yamamori, Chiharu Urano, Michitaka Maruyama +2 more

A 2 V Shapiro step with a current height of about 0.3 mA was successfully generated at 4.2 K with a single array including 65 536 Nb/TiN/Nb Josephson junctions under microwave irradiation at 16 GHz. The critical current density was 89 kA cm − 2 , and the junction size was 3 µm. The n = 1 step height decreased exponentially as the number of junctions N increased when the number of junctions was less than 30 000, a result that agreed well with the dissipated junction model. On the other hand, the step height was nearly constant when the number of junctions was more than about 30 000, a figure much larger than that theoretically calculated from the model. Using an array including such a large number of Josephson junctions represents a promising way for ac waveform synthesis to increase output voltage to about 1 V rms .

Superconductor Science and Technology•Jun 16, 2010•5 citations

Feasibility of the Josephson voltage and current standards on a single chip

Rais S. Shaikhaidarov, Ilya Antonov, Kyung Ho Kim +5 more

The quantum Josephson voltage standard is well established across the metrology community for many years. It relies on the synchronization of the flux tunneling in the S/I/S Josephson junctions (JJ) with the microwave radiation (MW) of frequency f such that V=Φ0fm, where m = 0, 1, 2, …. The phenomenon is called the Shapiro steps. Together with the quantum Hall resistance standard, the voltage standard forms the foundation of electrostatic metrology. The current is then defined as the ratio of the voltage and resistance. Realization of the quantum current standard would close the electrostatic metrological triangle of voltage–resistance–current. The current quantization I=2efm, the inverse Shapiro steps, was recently shown using the superconducting nanowires and small JJ. The effect is a synchronization of the MW with the Cooper pair tunneling. This paves the way to combine the JJ voltage and current standards on the same chip and demonstrate feasibility of the multi-standard operation. We show the voltage and current quantization on the same chip up to frequency of 10 GHz, corresponding to the amplitudes ∼ 20.67 μV and ∼ 3.2 nA, respectively. The accuracy of the voltage and current quantization, however, is relatively low, 35 and 100 ppk, respectively. We discuss measures to optimize the JJs, circuit, and environment to boost the amplitude and accuracy of the standards.

arXiv:2410.11018•Applied Physics Letters•Sep 16, 2024•6 citations

Metrological Study of YBCO Josephson Junction Arrays Integrated in a Fabry-Perot Resonator

A. Sosso, Domenico Andreone, V. Lacquaniti +3 more

The application of high temperature superconductor Josephson junctions to voltage metrology is promising for many reasons, beyond the evident advantage of simplified cryogenics and reduced costs of the apparatus. Owing to their intrinsic non-hysteretic behavior, arrays of shunted bicrystal YBCO junctions are particularly interesting for the realization of an AC voltage standard with quantum accuracy. Moreover, shunted bicrystal YBCO junctions arrays are advantageous because of the reduced area of the junctions, the wide range of characteristic voltages, and large critical currents. However, some specific problems arise, like possible effects related to the higher operating temperature. Furthermore, fabrication technology sets tight constraints on the design of structures for the distribution of microwave currents along the array junctions. We investigated the step properties under millimeter wave irradiation at frequencies about 75 GHz of HTS junction and arrays prepared on bicrystal substrates having grain boundaries. High sensitivity techniques were adopted to evaluate the step flatness at nV level and assess the accuracy of the step voltage. A new method that makes use of an open resonator, was implemented to irradiate the array, providing synchronization of a large number of junctions.

IEEE Transactions on Applied Superconductivity•Jun 1, 2007•8 citations

Model analysis for a current-step-like structure in a high Tc Josephson device coupled to a microwave signal

Yoshinao Mizugaki, Jian Chen

High Tc Josephson junctions have IcRn products as large as a few mV at liquid helium temperature, and hence, the frequency normalized by IcRn∕Φ0 becomes on the order of 10−3 for a gigahertz (GHz) microwave signal. (Here, Ic, Rn, and Φ0 are the critical current, the normal resistance, and a flux quantum, respectively.) It is well known that a microwave-current-driven Josephson junction does not exhibit clear Shapiro steps under such low frequency conditions. Instead of Shapiro steps, however, we often observe a current-step-like structure in the current–voltage curve of YBa2Cu3O7−δ grain boundary Josephson junctions coupled to a GHz signal. In this article, we present a model analysis for such current-step-like structures. Two types of device models are employed: a simple resistively and capacitively shunted junction model and a rf-field-driven two-junction superconducting quantum interference device model. Numerical results of the latter model agree with the experimental results, which indicates that the envelope of small Shapiro steps, including the effects of microwave-induced motion of flux quanta, appears as a current-step-like structure in a high Tc Josephson device coupled to a GHz microwave.

Journal of Applied Physics•Mar 8, 2005•3 citations
Quantum metrology based on Josephson junction array reproduces the most accurate desired voltage by far, therefore being introduced to provide voltage standards worldwide. In this work, we quantitatively analyzed the dependence of the first Shapiro step height of the junction array at 50 GHz on the parameter spread of 10,000 Josephson junctions by numerical simulation with resistively shunted junction model. The results indicate an upper limit spread of the critical current and resistance of the Josephson junctions. Specifically, to keep the maximum first Shapiro step above 0.88 mA, the critical current standard deviation, σσσ, should not exceed 25%, and for it to stay above 0.6 mA, the resistance standard deviation should not exceed 1.5%.
Quantum metrology based on Josephson junction array reproduces the most accurate desired voltage by far, therefore being introduced to provide voltage standards worldwide. In this work, we quantitatively analyzed the dependence of the first Shapiro step height of the junction array at 70 GHz on the parameter spread of 8,000 Josephson junctions with an average critical current (Ic) of 3.5 mA and an average normal state resistance (Rn) of 40 mΩ, using numerical simulations based on the resistively shunted junction (RSJ) model. The results indicate an upper limit spread of the Ic and Rn of the Josephson junctions. Specifically, to keep the maximum first Shapiro step above 0.9 mA, the Ic standard deviation, σ, should not exceed 25%, and for it to stay above 0.5 mA, the Rn deviation should not exceed 9%. This analysis specifically clarifies the required level of manufacturing process sophistication for superconducting devices to realize high-temperature superconducting (HTS) quantum-based voltage standards.
Abstract The dynamics of overdamped Josephson junctions under varying microwave-driving conditions have been studied through numerical simulations using the resistively-shunted junction model, with a focus on primary voltage metrology applications, where a significantly high number of series-connected junctions and stringent uniformity of their electrical parameters are required. The aim is to determine the optimal junction characteristics and external microwave (rf) parameters that maximize the width of quantum voltage levels (Shapiro steps) from order n = 0 to n > 1. Both the rf and dc power requirements, along with the junction parameter spread and power attenuation, are analyzed as key factors that need to be optimized for improved performance of the quantum device. This work aims to advance the development of next-generation programmable Josephson voltage standards with logic architectures that surpass the conventional binary and ternary codifications used in present quantum voltage arrays, while significantly reducing the overall number of junctions as well as the number of sub-arrays and bias lines. Existing technologies exploiting n = 0 and n = ± 1 voltage steps are first discussed and analyzed to verify the validity of the simulation model. They are then further investigated to extend their usability with multi-order quantum steps for n up to 3. From the simulation results, it follows that present junction technologies may be employed with no modifications for the simultaneous operation of quantum steps up to n = 2, although optimal power efficiency would require a retrimming of the junction’s electrical parameters. On the contrary, extending the highest step order to n = 3 strictly requires the junction’s characteristic parameters to be properly adjusted to maintain sustainable power levels as well as acceptable quantum-locking ranges.
A 2 V Shapiro step with a current height of about 0.3 mA was successfully generated at 4.2 K with a single array including 65 536 Nb/TiN/Nb Josephson junctions under microwave irradiation at 16 GHz. The critical current density was 89 kA cm − 2 , and the junction size was 3 µm. The n = 1 step height decreased exponentially as the number of junctions N increased when the number of junctions was less than 30 000, a result that agreed well with the dissipated junction model. On the other hand, the step height was nearly constant when the number of junctions was more than about 30 000, a figure much larger than that theoretically calculated from the model. Using an array including such a large number of Josephson junctions represents a promising way for ac waveform synthesis to increase output voltage to about 1 V rms .
The quantum Josephson voltage standard is well established across the metrology community for many years. It relies on the synchronization of the flux tunneling in the S/I/S Josephson junctions (JJ) with the microwave radiation (MW) of frequency f such that V=Φ0fm, where m = 0, 1, 2, …. The phenomenon is called the Shapiro steps. Together with the quantum Hall resistance standard, the voltage standard forms the foundation of electrostatic metrology. The current is then defined as the ratio of the voltage and resistance. Realization of the quantum current standard would close the electrostatic metrological triangle of voltage–resistance–current. The current quantization I=2efm, the inverse Shapiro steps, was recently shown using the superconducting nanowires and small JJ. The effect is a synchronization of the MW with the Cooper pair tunneling. This paves the way to combine the JJ voltage and current standards on the same chip and demonstrate feasibility of the multi-standard operation. We show the voltage and current quantization on the same chip up to frequency of 10 GHz, corresponding to the amplitudes ∼ 20.67 μV and ∼ 3.2 nA, respectively. The accuracy of the voltage and current quantization, however, is relatively low, 35 and 100 ppk, respectively. We discuss measures to optimize the JJs, circuit, and environment to boost the amplitude and accuracy of the standards.
The application of high temperature superconductor Josephson junctions to voltage metrology is promising for many reasons, beyond the evident advantage of simplified cryogenics and reduced costs of the apparatus. Owing to their intrinsic non-hysteretic behavior, arrays of shunted bicrystal YBCO junctions are particularly interesting for the realization of an AC voltage standard with quantum accuracy. Moreover, shunted bicrystal YBCO junctions arrays are advantageous because of the reduced area of the junctions, the wide range of characteristic voltages, and large critical currents. However, some specific problems arise, like possible effects related to the higher operating temperature. Furthermore, fabrication technology sets tight constraints on the design of structures for the distribution of microwave currents along the array junctions. We investigated the step properties under millimeter wave irradiation at frequencies about 75 GHz of HTS junction and arrays prepared on bicrystal substrates having grain boundaries. High sensitivity techniques were adopted to evaluate the step flatness at nV level and assess the accuracy of the step voltage. A new method that makes use of an open resonator, was implemented to irradiate the array, providing synchronization of a large number of junctions.
High Tc Josephson junctions have IcRn products as large as a few mV at liquid helium temperature, and hence, the frequency normalized by IcRn∕Φ0 becomes on the order of 10−3 for a gigahertz (GHz) microwave signal. (Here, Ic, Rn, and Φ0 are the critical current, the normal resistance, and a flux quantum, respectively.) It is well known that a microwave-current-driven Josephson junction does not exhibit clear Shapiro steps under such low frequency conditions. Instead of Shapiro steps, however, we often observe a current-step-like structure in the current–voltage curve of YBa2Cu3O7−δ grain boundary Josephson junctions coupled to a GHz signal. In this article, we present a model analysis for such current-step-like structures. Two types of device models are employed: a simple resistively and capacitively shunted junction model and a rf-field-driven two-junction superconducting quantum interference device model. Numerical results of the latter model agree with the experimental results, which indicates that the envelope of small Shapiro steps, including the effects of microwave-induced motion of flux quanta, appears as a current-step-like structure in a high Tc Josephson device coupled to a GHz microwave.