The Josephson effect has been utilized for primary voltage standards, since it can generate precise voltage guaranteed by quantum mechanics [1]. In the primary Josephson voltage standard (JVS) systems, dedicated dewars filled with liquid helium or mechanical cryocoolers with magnetic shielding and low-noise wiring are considered indispensable, which prevents us to directly use the quantized voltage signals for the other low temperature measurements without signal cables passing through the room temperature environments.

High quality voltage references in cryogenic conditions will be utilized for precise electrical measurements in basic physics and metrology fields [2]. In the series of our study, we have been trying to realize stable reference voltage sources in low temperatures and high magnetic fields conditions by implementing an optimally-shielded JVS device in a dilution refrigerator.

In our previous study, we developed a temperature-control module for the JVS device implemented on the 4 K stage of a dilution refrigerator, and confirmed generation of quantized voltages with stable temperature control under no magnetic field condition [3]. In this presentation, we report the optimized design and simulation of the effects of magnetic shields on the JVS device operation under a magnetic field. Our target is to reduce the residual magnetic field inside the shields to the level lower than the magnitude of the geomagnetic field, i.e., approximately 50 µT, even with an external high magnetic field. In the simulation, we assumed 10 T magnetic field generated by a superconducting magnet mounted at the bottom of the mixing chamber stage of the refrigerator. Given the calculation, we reached the optimal combination of shielding materials (high-magnetic-permeability metal/Pb/Nb) and thicknesses of them, the box of which showed that the simulated residual magnetic field in the vicinity of the JVS can reduce to less than 10 µT. A prototype magnetic shield box based on the simulation result has been fabricated, and it will be experimentally confirmed the performance.

This work was supported by JSPS KAKENHI Grant Number JP18H05258.

 [1]　M. Maruyama, A. Iwasa, H. Yamamori, S.-F. Chen, C. Urano, and N.-H. Kaneko, “Calibration System for Zener Voltage Standards Using a 10 V Programmable Josephson Voltage Standard at NMIJ, “ IEEE Trans. Instrum. Meas., vol. 64, no. 6, pp. 1606−1612, Jun. 2015.

[2]　T. J. B. M. Janssen, J. M. Williams, N. E. Fletcher, R. Goebel, A. Tzalenchuk, R. Yakimova, S. Lara-Avila, S. Kubatkin, and V.I. Fal'ko, “Precision comparison of the quantum Hall effect in graphene and gallium arsenide, “ Metrologia, vol. 49, no. 3, pp. 294−306, Mar. 2012.

[3]　D. Matsumaru, S. Nakamura, Z. Jia, M. Maruyama, and N.-H. Kaneko, “Operation of a Josephson voltage standard device cooled with a dilution refrigerator,” ISS2021 Conf. Digest, pp. 1−1, Nov. 2021.

Keywords: Josephson effect, voltage standard, magnetic shielding, magnetic field